Factors of 32400

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How to find factors of a number

1. Steps to find factors of 32400 using Division Method

Find all the numbers which can divide 32400 without leaving any remainder, starting from number 1 upto 16200 (half of 32400). The number 1 and the number (32400) itself are always factors of the given number (32400).
Note down all such number. All of those numbers are factors of 32400.

Example: Find factors of 32400

Divide 32400 by 1: 32400 ÷ 1 : Remainder = 0
Divide 32400 by 2: 32400 ÷ 2 : Remainder = 0
Divide 32400 by 3: 32400 ÷ 3 : Remainder = 0
Divide 32400 by 4: 32400 ÷ 4 : Remainder = 0
Divide 32400 by 5: 32400 ÷ 5 : Remainder = 0
Divide 32400 by 6: 32400 ÷ 6 : Remainder = 0
Divide 32400 by 8: 32400 ÷ 8 : Remainder = 0
Divide 32400 by 9: 32400 ÷ 9 : Remainder = 0
Divide 32400 by 10: 32400 ÷ 10 : Remainder = 0
Divide 32400 by 12: 32400 ÷ 12 : Remainder = 0
Divide 32400 by 15: 32400 ÷ 15 : Remainder = 0
Divide 32400 by 16: 32400 ÷ 16 : Remainder = 0
Divide 32400 by 18: 32400 ÷ 18 : Remainder = 0
Divide 32400 by 20: 32400 ÷ 20 : Remainder = 0
Divide 32400 by 24: 32400 ÷ 24 : Remainder = 0
Divide 32400 by 25: 32400 ÷ 25 : Remainder = 0
Divide 32400 by 27: 32400 ÷ 27 : Remainder = 0
Divide 32400 by 30: 32400 ÷ 30 : Remainder = 0
Divide 32400 by 36: 32400 ÷ 36 : Remainder = 0
Divide 32400 by 40: 32400 ÷ 40 : Remainder = 0
Divide 32400 by 45: 32400 ÷ 45 : Remainder = 0
Divide 32400 by 48: 32400 ÷ 48 : Remainder = 0
Divide 32400 by 50: 32400 ÷ 50 : Remainder = 0
Divide 32400 by 54: 32400 ÷ 54 : Remainder = 0
Divide 32400 by 60: 32400 ÷ 60 : Remainder = 0
Divide 32400 by 72: 32400 ÷ 72 : Remainder = 0
Divide 32400 by 75: 32400 ÷ 75 : Remainder = 0
Divide 32400 by 80: 32400 ÷ 80 : Remainder = 0
Divide 32400 by 81: 32400 ÷ 81 : Remainder = 0
Divide 32400 by 90: 32400 ÷ 90 : Remainder = 0
Divide 32400 by 100: 32400 ÷ 100 : Remainder = 0
Divide 32400 by 108: 32400 ÷ 108 : Remainder = 0
Divide 32400 by 120: 32400 ÷ 120 : Remainder = 0
Divide 32400 by 135: 32400 ÷ 135 : Remainder = 0
Divide 32400 by 144: 32400 ÷ 144 : Remainder = 0
Divide 32400 by 150: 32400 ÷ 150 : Remainder = 0
Divide 32400 by 162: 32400 ÷ 162 : Remainder = 0
Divide 32400 by 180: 32400 ÷ 180 : Remainder = 0
Divide 32400 by 200: 32400 ÷ 200 : Remainder = 0
Divide 32400 by 216: 32400 ÷ 216 : Remainder = 0
Divide 32400 by 225: 32400 ÷ 225 : Remainder = 0
Divide 32400 by 240: 32400 ÷ 240 : Remainder = 0
Divide 32400 by 270: 32400 ÷ 270 : Remainder = 0
Divide 32400 by 300: 32400 ÷ 300 : Remainder = 0
Divide 32400 by 324: 32400 ÷ 324 : Remainder = 0
Divide 32400 by 360: 32400 ÷ 360 : Remainder = 0
Divide 32400 by 400: 32400 ÷ 400 : Remainder = 0
Divide 32400 by 405: 32400 ÷ 405 : Remainder = 0
Divide 32400 by 432: 32400 ÷ 432 : Remainder = 0
Divide 32400 by 450: 32400 ÷ 450 : Remainder = 0
Divide 32400 by 540: 32400 ÷ 540 : Remainder = 0
Divide 32400 by 600: 32400 ÷ 600 : Remainder = 0
Divide 32400 by 648: 32400 ÷ 648 : Remainder = 0
Divide 32400 by 675: 32400 ÷ 675 : Remainder = 0
Divide 32400 by 720: 32400 ÷ 720 : Remainder = 0
Divide 32400 by 810: 32400 ÷ 810 : Remainder = 0
Divide 32400 by 900: 32400 ÷ 900 : Remainder = 0
Divide 32400 by 1080: 32400 ÷ 1080 : Remainder = 0
Divide 32400 by 1200: 32400 ÷ 1200 : Remainder = 0
Divide 32400 by 1296: 32400 ÷ 1296 : Remainder = 0
Divide 32400 by 1350: 32400 ÷ 1350 : Remainder = 0
Divide 32400 by 1620: 32400 ÷ 1620 : Remainder = 0
Divide 32400 by 1800: 32400 ÷ 1800 : Remainder = 0
Divide 32400 by 2025: 32400 ÷ 2025 : Remainder = 0
Divide 32400 by 2160: 32400 ÷ 2160 : Remainder = 0
Divide 32400 by 2700: 32400 ÷ 2700 : Remainder = 0
Divide 32400 by 3240: 32400 ÷ 3240 : Remainder = 0
Divide 32400 by 3600: 32400 ÷ 3600 : Remainder = 0
Divide 32400 by 4050: 32400 ÷ 4050 : Remainder = 0
Divide 32400 by 5400: 32400 ÷ 5400 : Remainder = 0
Divide 32400 by 6480: 32400 ÷ 6480 : Remainder = 0
Divide 32400 by 8100: 32400 ÷ 8100 : Remainder = 0
Divide 32400 by 10800: 32400 ÷ 10800 : Remainder = 0
Divide 32400 by 16200: 32400 ÷ 16200 : Remainder = 0
Divide 32400 by 32400: 32400 ÷ 32400 : Remainder = 0

Hence, Factors of 32400 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 27, 30, 36, 40, 45, 48, 50, 54, 60, 72, 75, 80, 81, 90, 100, 108, 120, 135, 144, 150, 162, 180, 200, 216, 225, 240, 270, 300, 324, 360, 400, 405, 432, 450, 540, 600, 648, 675, 720, 810, 900, 1080, 1200, 1296, 1350, 1620, 1800, 2025, 2160, 2700, 3240, 3600, 4050, 5400, 6480, 8100, 10800, 16200, and 32400

2. Steps to find factors of 32400 using Prime Factorization

A prime number is a number that has exactly two factors, 1 and the number itself. Prime factorization of a number means breaking down of the number into the form of products of its prime factors.

There are two different methods that can be used for the prime factorization.

Method 1: Division Method

To find the primefactors of 32400 using the division method, follow these steps:

Step 1. Start dividing 32400 by the smallest prime number, i.e., 2, 3, 5, and so on. Find the smallest prime factor of the number.
Step 2. After finding the smallest prime factor of the number 32400, which is 2. Divide 32400 by 2 to obtain the quotient (16200).
32400 ÷ 2 = 16200
Step 3. Repeat step 1 with the obtained quotient (16200).
16200 ÷ 2 = 8100

8100 ÷ 2 = 4050

4050 ÷ 2 = 2025

2025 ÷ 3 = 675

675 ÷ 3 = 225

225 ÷ 3 = 75

75 ÷ 3 = 25

25 ÷ 5 = 5

5 ÷ 5 = 1

So, the prime factorization of 32400 is, 32400 = 2 x 2 x 2 x 2 x 3 x 3 x 3 x 3 x 5 x 5.

Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 32400 as shown below:

So, the prime factorization of 32400 is, 32400 = 2 x 2 x 2 x 2 x 3 x 3 x 3 x 3 x 5 x 5.

3. Find factors of 32400 in Pairs

Pair factors of a number are any two numbers which, which on multiplying together, give that number as a result. The pair factors of 32400 would be the two numbers which, when multiplied, give 32400 as the result.

The following table represents the calculation of factors of 32400 in pairs:

Factor Pair	Pair Factorization
1 and 32400	1 x 32400 = 32400
2 and 16200	2 x 16200 = 32400
3 and 10800	3 x 10800 = 32400
4 and 8100	4 x 8100 = 32400
5 and 6480	5 x 6480 = 32400
6 and 5400	6 x 5400 = 32400
8 and 4050	8 x 4050 = 32400
9 and 3600	9 x 3600 = 32400
10 and 3240	10 x 3240 = 32400
12 and 2700	12 x 2700 = 32400
15 and 2160	15 x 2160 = 32400
16 and 2025	16 x 2025 = 32400
18 and 1800	18 x 1800 = 32400
20 and 1620	20 x 1620 = 32400
24 and 1350	24 x 1350 = 32400
25 and 1296	25 x 1296 = 32400
27 and 1200	27 x 1200 = 32400
30 and 1080	30 x 1080 = 32400
36 and 900	36 x 900 = 32400
40 and 810	40 x 810 = 32400
45 and 720	45 x 720 = 32400
48 and 675	48 x 675 = 32400
50 and 648	50 x 648 = 32400
54 and 600	54 x 600 = 32400
60 and 540	60 x 540 = 32400
72 and 450	72 x 450 = 32400
75 and 432	75 x 432 = 32400
80 and 405	80 x 405 = 32400
81 and 400	81 x 400 = 32400
90 and 360	90 x 360 = 32400
100 and 324	100 x 324 = 32400
108 and 300	108 x 300 = 32400
120 and 270	120 x 270 = 32400
135 and 240	135 x 240 = 32400
144 and 225	144 x 225 = 32400
150 and 216	150 x 216 = 32400
162 and 200	162 x 200 = 32400
180 and 180	180 x 180 = 32400

Since the product of two negative numbers gives a positive number, the product of the negative values of both the numbers in a pair factor will also give 32400. They are called negative pair factors.

Hence, the negative pairs of 32400 would be ( -1 , -32400 ) , ( -2 , -16200 ) , ( -3 , -10800 ) , ( -4 , -8100 ) , ( -5 , -6480 ) , ( -6 , -5400 ) , ( -8 , -4050 ) , ( -9 , -3600 ) , ( -10 , -3240 ) , ( -12 , -2700 ) , ( -15 , -2160 ) , ( -16 , -2025 ) , ( -18 , -1800 ) , ( -20 , -1620 ) , ( -24 , -1350 ) , ( -25 , -1296 ) , ( -27 , -1200 ) , ( -30 , -1080 ) , ( -36 , -900 ) , ( -40 , -810 ) , ( -45 , -720 ) , ( -48 , -675 ) , ( -50 , -648 ) , ( -54 , -600 ) , ( -60 , -540 ) , ( -72 , -450 ) , ( -75 , -432 ) , ( -80 , -405 ) , ( -81 , -400 ) , ( -90 , -360 ) , ( -100 , -324 ) , ( -108 , -300 ) , ( -120 , -270 ) , ( -135 , -240 ) , ( -144 , -225 ) , ( -150 , -216 ) , ( -162 , -200 ) and ( -180 , -180 ) .

What are factors?

In mathematics, a factor is that number which divides into another number exactly, without leaving a remainder. A factor of a number can be positive or negative.

Properties of factors

Each number is a factor of itself. Eg. 32400 is a factor of itself.
1 is a factor of every number. Eg. 1 is a factor of 32400.
Every number is a factor of zero (0), since 32400 x 0 = 0.
Every number other than 1 has at least two factors, namely the number itself and 1.
Every factor of a number is an exact divisor of that number, example 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 27, 30, 36, 40, 45, 48, 50, 54, 60, 72, 75, 80, 81, 90, 100, 108, 120, 135, 144, 150, 162, 180, 200, 216, 225, 240, 270, 300, 324, 360, 400, 405, 432, 450, 540, 600, 648, 675, 720, 810, 900, 1080, 1200, 1296, 1350, 1620, 1800, 2025, 2160, 2700, 3240, 3600, 4050, 5400, 6480, 8100, 10800, 16200, 32400 are exact divisors of 32400.
Factors of 32400 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 27, 30, 36, 40, 45, 48, 50, 54, 60, 72, 75, 80, 81, 90, 100, 108, 120, 135, 144, 150, 162, 180, 200, 216, 225, 240, 270, 300, 324, 360, 400, 405, 432, 450, 540, 600, 648, 675, 720, 810, 900, 1080, 1200, 1296, 1350, 1620, 1800, 2025, 2160, 2700, 3240, 3600, 4050, 5400, 6480, 8100, 10800, 16200, 32400. Each factor divides 32400 without leaving a remainder.
Every factor of a number is less than or equal to the number, eg. 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 27, 30, 36, 40, 45, 48, 50, 54, 60, 72, 75, 80, 81, 90, 100, 108, 120, 135, 144, 150, 162, 180, 200, 216, 225, 240, 270, 300, 324, 360, 400, 405, 432, 450, 540, 600, 648, 675, 720, 810, 900, 1080, 1200, 1296, 1350, 1620, 1800, 2025, 2160, 2700, 3240, 3600, 4050, 5400, 6480, 8100, 10800, 16200, 32400 are all less than or equal to 32400.

Frequently Asked Questions

Which is the smallest prime factor of 32400?
Smallest prime factor of 32400 is 2.
Is 32400 a perfect square?
Yes 32400 is a perfect square.
What are five multiples of 32400?
First five multiples of 32400 are 64800, 97200, 129600, 162000, 194400.
What is prime factorization of 32400?
Prime factorization of 32400 is 2 x 2 x 2 x 2 x 3 x 3 x 3 x 3 x 5 x 5.
What are factors of 32400?
Factors of 32400 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 27, 30, 36, 40, 45, 48, 50, 54, 60, 72, 75, 80, 81, 90, 100, 108, 120, 135, 144, 150, 162, 180, 200, 216, 225, 240, 270, 300, 324, 360, 400, 405, 432, 450, 540, 600, 648, 675, 720, 810, 900, 1080, 1200, 1296, 1350, 1620, 1800, 2025, 2160, 2700, 3240, 3600, 4050, 5400, 6480, 8100, 10800, 16200, 32400.
How do you find factors of a negative number? ( eg. -32400 )?
Factors of -32400 are -1, -2, -3, -4, -5, -6, -8, -9, -10, -12, -15, -16, -18, -20, -24, -25, -27, -30, -36, -40, -45, -48, -50, -54, -60, -72, -75, -80, -81, -90, -100, -108, -120, -135, -144, -150, -162, -180, -200, -216, -225, -240, -270, -300, -324, -360, -400, -405, -432, -450, -540, -600, -648, -675, -720, -810, -900, -1080, -1200, -1296, -1350, -1620, -1800, -2025, -2160, -2700, -3240, -3600, -4050, -5400, -6480, -8100, -10800, -16200, -32400.
Is 32400 a whole number?
Yes 32400 is a whole number.
Which is greatest factor of 32400?
The greatest factor of 32400 is 16200.
What are the prime factors of 32400?
The factors of 32400 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 27, 30, 36, 40, 45, 48, 50, 54, 60, 72, 75, 80, 81, 90, 100, 108, 120, 135, 144, 150, 162, 180, 200, 216, 225, 240, 270, 300, 324, 360, 400, 405, 432, 450, 540, 600, 648, 675, 720, 810, 900, 1080, 1200, 1296, 1350, 1620, 1800, 2025, 2160, 2700, 3240, 3600, 4050, 5400, 6480, 8100, 10800, 16200, 32400.
Prime factors of 32400 are 2, 2, 2, 2, 3, 3, 3, 3, 5, 5.

Examples of Factors

Ariel has been assigned the task to find the product of all the prime factors of 32400. Can you help her?

Prime factors of 32400 are 2, 2, 2, 2, 3, 3, 3, 3, 5, 5.
Hence, the product of prime factors of 30.

Can you help Rubel to find out the product of the even factors of 32400?

Factors of 32400 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 27, 30, 36, 40, 45, 48, 50, 54, 60, 72, 75, 80, 81, 90, 100, 108, 120, 135, 144, 150, 162, 180, 200, 216, 225, 240, 270, 300, 324, 360, 400, 405, 432, 450, 540, 600, 648, 675, 720, 810, 900, 1080, 1200, 1296, 1350, 1620, 1800, 2025, 2160, 2700, 3240, 3600, 4050, 5400, 6480, 8100, 10800, 16200, 32400.
Even factors of 32400 are 2, 4, 6, 8, 10, 12, 16, 18, 20, 24, 30, 36, 40, 48, 50, 54, 60, 72, 80, 90, 100, 108, 120, 144, 150, 162, 180, 200, 216, 240, 270, 300, 324, 360, 400, 432, 450, 540, 600, 648, 720, 810, 900, 1080, 1200, 1296, 1350, 1620, 1800, 2160, 2700, 3240, 3600, 4050, 5400, 6480, 8100, 10800, 16200, 32400.
Hence, product of even factors of 32400 is; 2 x 4 x 6 x 8 x 10 x 12 x 16 x 18 x 20 x 24 x 30 x 36 x 40 x 48 x 50 x 54 x 60 x 72 x 80 x 90 x 100 x 108 x 120 x 144 x 150 x 162 x 180 x 200 x 216 x 240 x 270 x 300 x 324 x 360 x 400 x 432 x 450 x 540 x 600 x 648 x 720 x 810 x 900 x 1080 x 1200 x 1296 x 1350 x 1620 x 1800 x 2160 x 2700 x 3240 x 3600 x 4050 x 5400 x 6480 x 8100 x 10800 x 16200 x 32400 = 2.2245910012723034e+144.

Joy wants to calculate mean of all the factors of 32400. Help him in finding the mean of 32400.

Factors of 32400 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 27, 30, 36, 40, 45, 48, 50, 54, 60, 72, 75, 80, 81, 90, 100, 108, 120, 135, 144, 150, 162, 180, 200, 216, 225, 240, 270, 300, 324, 360, 400, 405, 432, 450, 540, 600, 648, 675, 720, 810, 900, 1080, 1200, 1296, 1350, 1620, 1800, 2025, 2160, 2700, 3240, 3600, 4050, 5400, 6480, 8100, 10800, 16200, 32400.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 32400 is 1 + 2 + 3 + 4 + 5 + 6 + 8 + 9 + 10 + 12 + 15 + 16 + 18 + 20 + 24 + 25 + 27 + 30 + 36 + 40 + 45 + 48 + 50 + 54 + 60 + 72 + 75 + 80 + 81 + 90 + 100 + 108 + 120 + 135 + 144 + 150 + 162 + 180 + 200 + 216 + 225 + 240 + 270 + 300 + 324 + 360 + 400 + 405 + 432 + 450 + 540 + 600 + 648 + 675 + 720 + 810 + 900 + 1080 + 1200 + 1296 + 1350 + 1620 + 1800 + 2025 + 2160 + 2700 + 3240 + 3600 + 4050 + 5400 + 6480 + 8100 + 10800 + 16200 + 32400 = 116281.
Hence, the mean of factors of 32400 is 116281 ÷ 75 = 1550.41.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 32400? Help her in writing all the factors.

Positive factors are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 27, 30, 36, 40, 45, 48, 50, 54, 60, 72, 75, 80, 81, 90, 100, 108, 120, 135, 144, 150, 162, 180, 200, 216, 225, 240, 270, 300, 324, 360, 400, 405, 432, 450, 540, 600, 648, 675, 720, 810, 900, 1080, 1200, 1296, 1350, 1620, 1800, 2025, 2160, 2700, 3240, 3600, 4050, 5400, 6480, 8100, 10800, 16200, 32400.
Negative factors are -1, -2, -3, -4, -5, -6, -8, -9, -10, -12, -15, -16, -18, -20, -24, -25, -27, -30, -36, -40, -45, -48, -50, -54, -60, -72, -75, -80, -81, -90, -100, -108, -120, -135, -144, -150, -162, -180, -200, -216, -225, -240, -270, -300, -324, -360, -400, -405, -432, -450, -540, -600, -648, -675, -720, -810, -900, -1080, -1200, -1296, -1350, -1620, -1800, -2025, -2160, -2700, -3240, -3600, -4050, -5400, -6480, -8100, -10800, -16200, -32400.

How many factors are there for 32400?

Joey wants to write all the prime factors of 32400 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 32400 are 2, 2, 2, 2, 3, 3, 3, 3, 5, 5.
So in exponential form it can be written as 2⁴ x 3⁴ x 5².

Kevin has been asked to write 74 factor(s) of 32400. Can you predict the answer?

74 factor(s) of 32400 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 27, 30, 36, 40, 45, 48, 50, 54, 60, 72, 75, 80, 81, 90, 100, 108, 120, 135, 144, 150, 162, 180, 200, 216, 225, 240, 270, 300, 324, 360, 400, 405, 432, 450, 540, 600, 648, 675, 720, 810, 900, 1080, 1200, 1296, 1350, 1620, 1800, 2025, 2160, 2700, 3240, 3600, 4050, 5400, 6480, 8100, 10800, 16200.