Factors of 21600

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How to find factors of a number

1. Steps to find factors of 21600 using Division Method

Find all the numbers which can divide 21600 without leaving any remainder, starting from number 1 upto 10800 (half of 21600). The number 1 and the number (21600) itself are always factors of the given number (21600).
Note down all such number. All of those numbers are factors of 21600.

Example: Find factors of 21600

Divide 21600 by 1: 21600 ÷ 1 : Remainder = 0
Divide 21600 by 2: 21600 ÷ 2 : Remainder = 0
Divide 21600 by 3: 21600 ÷ 3 : Remainder = 0
Divide 21600 by 4: 21600 ÷ 4 : Remainder = 0
Divide 21600 by 5: 21600 ÷ 5 : Remainder = 0
Divide 21600 by 6: 21600 ÷ 6 : Remainder = 0
Divide 21600 by 8: 21600 ÷ 8 : Remainder = 0
Divide 21600 by 9: 21600 ÷ 9 : Remainder = 0
Divide 21600 by 10: 21600 ÷ 10 : Remainder = 0
Divide 21600 by 12: 21600 ÷ 12 : Remainder = 0
Divide 21600 by 15: 21600 ÷ 15 : Remainder = 0
Divide 21600 by 16: 21600 ÷ 16 : Remainder = 0
Divide 21600 by 18: 21600 ÷ 18 : Remainder = 0
Divide 21600 by 20: 21600 ÷ 20 : Remainder = 0
Divide 21600 by 24: 21600 ÷ 24 : Remainder = 0
Divide 21600 by 25: 21600 ÷ 25 : Remainder = 0
Divide 21600 by 27: 21600 ÷ 27 : Remainder = 0
Divide 21600 by 30: 21600 ÷ 30 : Remainder = 0
Divide 21600 by 32: 21600 ÷ 32 : Remainder = 0
Divide 21600 by 36: 21600 ÷ 36 : Remainder = 0
Divide 21600 by 40: 21600 ÷ 40 : Remainder = 0
Divide 21600 by 45: 21600 ÷ 45 : Remainder = 0
Divide 21600 by 48: 21600 ÷ 48 : Remainder = 0
Divide 21600 by 50: 21600 ÷ 50 : Remainder = 0
Divide 21600 by 54: 21600 ÷ 54 : Remainder = 0
Divide 21600 by 60: 21600 ÷ 60 : Remainder = 0
Divide 21600 by 72: 21600 ÷ 72 : Remainder = 0
Divide 21600 by 75: 21600 ÷ 75 : Remainder = 0
Divide 21600 by 80: 21600 ÷ 80 : Remainder = 0
Divide 21600 by 90: 21600 ÷ 90 : Remainder = 0
Divide 21600 by 96: 21600 ÷ 96 : Remainder = 0
Divide 21600 by 100: 21600 ÷ 100 : Remainder = 0
Divide 21600 by 108: 21600 ÷ 108 : Remainder = 0
Divide 21600 by 120: 21600 ÷ 120 : Remainder = 0
Divide 21600 by 135: 21600 ÷ 135 : Remainder = 0
Divide 21600 by 144: 21600 ÷ 144 : Remainder = 0
Divide 21600 by 150: 21600 ÷ 150 : Remainder = 0
Divide 21600 by 160: 21600 ÷ 160 : Remainder = 0
Divide 21600 by 180: 21600 ÷ 180 : Remainder = 0
Divide 21600 by 200: 21600 ÷ 200 : Remainder = 0
Divide 21600 by 216: 21600 ÷ 216 : Remainder = 0
Divide 21600 by 225: 21600 ÷ 225 : Remainder = 0
Divide 21600 by 240: 21600 ÷ 240 : Remainder = 0
Divide 21600 by 270: 21600 ÷ 270 : Remainder = 0
Divide 21600 by 288: 21600 ÷ 288 : Remainder = 0
Divide 21600 by 300: 21600 ÷ 300 : Remainder = 0
Divide 21600 by 360: 21600 ÷ 360 : Remainder = 0
Divide 21600 by 400: 21600 ÷ 400 : Remainder = 0
Divide 21600 by 432: 21600 ÷ 432 : Remainder = 0
Divide 21600 by 450: 21600 ÷ 450 : Remainder = 0
Divide 21600 by 480: 21600 ÷ 480 : Remainder = 0
Divide 21600 by 540: 21600 ÷ 540 : Remainder = 0
Divide 21600 by 600: 21600 ÷ 600 : Remainder = 0
Divide 21600 by 675: 21600 ÷ 675 : Remainder = 0
Divide 21600 by 720: 21600 ÷ 720 : Remainder = 0
Divide 21600 by 800: 21600 ÷ 800 : Remainder = 0
Divide 21600 by 864: 21600 ÷ 864 : Remainder = 0
Divide 21600 by 900: 21600 ÷ 900 : Remainder = 0
Divide 21600 by 1080: 21600 ÷ 1080 : Remainder = 0
Divide 21600 by 1200: 21600 ÷ 1200 : Remainder = 0
Divide 21600 by 1350: 21600 ÷ 1350 : Remainder = 0
Divide 21600 by 1440: 21600 ÷ 1440 : Remainder = 0
Divide 21600 by 1800: 21600 ÷ 1800 : Remainder = 0
Divide 21600 by 2160: 21600 ÷ 2160 : Remainder = 0
Divide 21600 by 2400: 21600 ÷ 2400 : Remainder = 0
Divide 21600 by 2700: 21600 ÷ 2700 : Remainder = 0
Divide 21600 by 3600: 21600 ÷ 3600 : Remainder = 0
Divide 21600 by 4320: 21600 ÷ 4320 : Remainder = 0
Divide 21600 by 5400: 21600 ÷ 5400 : Remainder = 0
Divide 21600 by 7200: 21600 ÷ 7200 : Remainder = 0
Divide 21600 by 10800: 21600 ÷ 10800 : Remainder = 0
Divide 21600 by 21600: 21600 ÷ 21600 : Remainder = 0

Hence, Factors of 21600 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 27, 30, 32, 36, 40, 45, 48, 50, 54, 60, 72, 75, 80, 90, 96, 100, 108, 120, 135, 144, 150, 160, 180, 200, 216, 225, 240, 270, 288, 300, 360, 400, 432, 450, 480, 540, 600, 675, 720, 800, 864, 900, 1080, 1200, 1350, 1440, 1800, 2160, 2400, 2700, 3600, 4320, 5400, 7200, 10800, and 21600

2. Steps to find factors of 21600 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 21600 using the division method, follow these steps:

Step 1. Start dividing 21600 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 21600, which is 2. Divide 21600 by 2 to obtain the quotient (10800).
21600 ÷ 2 = 10800
Step 3. Repeat step 1 with the obtained quotient (10800).
10800 ÷ 2 = 5400

5400 ÷ 2 = 2700

2700 ÷ 2 = 1350

1350 ÷ 2 = 675

675 ÷ 3 = 225

225 ÷ 3 = 75

75 ÷ 3 = 25

25 ÷ 5 = 5

5 ÷ 5 = 1

So, the prime factorization of 21600 is, 21600 = 2 x 2 x 2 x 2 x 2 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 21600 as shown below:

So, the prime factorization of 21600 is, 21600 = 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 5 x 5.

3. Find factors of 21600 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 21600 would be the two numbers which, when multiplied, give 21600 as the result.

The following table represents the calculation of factors of 21600 in pairs:

Factor Pair	Pair Factorization
1 and 21600	1 x 21600 = 21600
2 and 10800	2 x 10800 = 21600
3 and 7200	3 x 7200 = 21600
4 and 5400	4 x 5400 = 21600
5 and 4320	5 x 4320 = 21600
6 and 3600	6 x 3600 = 21600
8 and 2700	8 x 2700 = 21600
9 and 2400	9 x 2400 = 21600
10 and 2160	10 x 2160 = 21600
12 and 1800	12 x 1800 = 21600
15 and 1440	15 x 1440 = 21600
16 and 1350	16 x 1350 = 21600
18 and 1200	18 x 1200 = 21600
20 and 1080	20 x 1080 = 21600
24 and 900	24 x 900 = 21600
25 and 864	25 x 864 = 21600
27 and 800	27 x 800 = 21600
30 and 720	30 x 720 = 21600
32 and 675	32 x 675 = 21600
36 and 600	36 x 600 = 21600
40 and 540	40 x 540 = 21600
45 and 480	45 x 480 = 21600
48 and 450	48 x 450 = 21600
50 and 432	50 x 432 = 21600
54 and 400	54 x 400 = 21600
60 and 360	60 x 360 = 21600
72 and 300	72 x 300 = 21600
75 and 288	75 x 288 = 21600
80 and 270	80 x 270 = 21600
90 and 240	90 x 240 = 21600
96 and 225	96 x 225 = 21600
100 and 216	100 x 216 = 21600
108 and 200	108 x 200 = 21600
120 and 180	120 x 180 = 21600
135 and 160	135 x 160 = 21600
144 and 150	144 x 150 = 21600

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 21600. They are called negative pair factors.

Hence, the negative pairs of 21600 would be ( -1 , -21600 ) , ( -2 , -10800 ) , ( -3 , -7200 ) , ( -4 , -5400 ) , ( -5 , -4320 ) , ( -6 , -3600 ) , ( -8 , -2700 ) , ( -9 , -2400 ) , ( -10 , -2160 ) , ( -12 , -1800 ) , ( -15 , -1440 ) , ( -16 , -1350 ) , ( -18 , -1200 ) , ( -20 , -1080 ) , ( -24 , -900 ) , ( -25 , -864 ) , ( -27 , -800 ) , ( -30 , -720 ) , ( -32 , -675 ) , ( -36 , -600 ) , ( -40 , -540 ) , ( -45 , -480 ) , ( -48 , -450 ) , ( -50 , -432 ) , ( -54 , -400 ) , ( -60 , -360 ) , ( -72 , -300 ) , ( -75 , -288 ) , ( -80 , -270 ) , ( -90 , -240 ) , ( -96 , -225 ) , ( -100 , -216 ) , ( -108 , -200 ) , ( -120 , -180 ) , ( -135 , -160 ) and ( -144 , -150 ) .

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. 21600 is a factor of itself.
1 is a factor of every number. Eg. 1 is a factor of 21600.
Every number is a factor of zero (0), since 21600 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, 32, 36, 40, 45, 48, 50, 54, 60, 72, 75, 80, 90, 96, 100, 108, 120, 135, 144, 150, 160, 180, 200, 216, 225, 240, 270, 288, 300, 360, 400, 432, 450, 480, 540, 600, 675, 720, 800, 864, 900, 1080, 1200, 1350, 1440, 1800, 2160, 2400, 2700, 3600, 4320, 5400, 7200, 10800, 21600 are exact divisors of 21600.
Factors of 21600 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 27, 30, 32, 36, 40, 45, 48, 50, 54, 60, 72, 75, 80, 90, 96, 100, 108, 120, 135, 144, 150, 160, 180, 200, 216, 225, 240, 270, 288, 300, 360, 400, 432, 450, 480, 540, 600, 675, 720, 800, 864, 900, 1080, 1200, 1350, 1440, 1800, 2160, 2400, 2700, 3600, 4320, 5400, 7200, 10800, 21600. Each factor divides 21600 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, 32, 36, 40, 45, 48, 50, 54, 60, 72, 75, 80, 90, 96, 100, 108, 120, 135, 144, 150, 160, 180, 200, 216, 225, 240, 270, 288, 300, 360, 400, 432, 450, 480, 540, 600, 675, 720, 800, 864, 900, 1080, 1200, 1350, 1440, 1800, 2160, 2400, 2700, 3600, 4320, 5400, 7200, 10800, 21600 are all less than or equal to 21600.

Frequently Asked Questions

Which is the smallest prime factor of 21600?
Smallest prime factor of 21600 is 2.
Is 21600 a perfect square?
No 21600 is not a perfect square.
What are five multiples of 21600?
First five multiples of 21600 are 43200, 64800, 86400, 108000, 129600.
What is prime factorization of 21600?
Prime factorization of 21600 is 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 5 x 5.
What are factors of 21600?
Factors of 21600 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 27, 30, 32, 36, 40, 45, 48, 50, 54, 60, 72, 75, 80, 90, 96, 100, 108, 120, 135, 144, 150, 160, 180, 200, 216, 225, 240, 270, 288, 300, 360, 400, 432, 450, 480, 540, 600, 675, 720, 800, 864, 900, 1080, 1200, 1350, 1440, 1800, 2160, 2400, 2700, 3600, 4320, 5400, 7200, 10800, 21600.
How do you find factors of a negative number? ( eg. -21600 )?
Factors of -21600 are -1, -2, -3, -4, -5, -6, -8, -9, -10, -12, -15, -16, -18, -20, -24, -25, -27, -30, -32, -36, -40, -45, -48, -50, -54, -60, -72, -75, -80, -90, -96, -100, -108, -120, -135, -144, -150, -160, -180, -200, -216, -225, -240, -270, -288, -300, -360, -400, -432, -450, -480, -540, -600, -675, -720, -800, -864, -900, -1080, -1200, -1350, -1440, -1800, -2160, -2400, -2700, -3600, -4320, -5400, -7200, -10800, -21600.
Is 21600 a whole number?
Yes 21600 is a whole number.
Which is greatest factor of 21600?
The greatest factor of 21600 is 10800.
What are the prime factors of 21600?
The factors of 21600 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 27, 30, 32, 36, 40, 45, 48, 50, 54, 60, 72, 75, 80, 90, 96, 100, 108, 120, 135, 144, 150, 160, 180, 200, 216, 225, 240, 270, 288, 300, 360, 400, 432, 450, 480, 540, 600, 675, 720, 800, 864, 900, 1080, 1200, 1350, 1440, 1800, 2160, 2400, 2700, 3600, 4320, 5400, 7200, 10800, 21600.
Prime factors of 21600 are 2, 2, 2, 2, 2, 3, 3, 3, 5, 5.

Examples of Factors

Ariel has been assigned the task to find the product of all the prime factors of 21600. Can you help her?

Prime factors of 21600 are 2, 2, 2, 2, 2, 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 21600?

Factors of 21600 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 27, 30, 32, 36, 40, 45, 48, 50, 54, 60, 72, 75, 80, 90, 96, 100, 108, 120, 135, 144, 150, 160, 180, 200, 216, 225, 240, 270, 288, 300, 360, 400, 432, 450, 480, 540, 600, 675, 720, 800, 864, 900, 1080, 1200, 1350, 1440, 1800, 2160, 2400, 2700, 3600, 4320, 5400, 7200, 10800, 21600.
Even factors of 21600 are 2, 4, 6, 8, 10, 12, 16, 18, 20, 24, 30, 32, 36, 40, 48, 50, 54, 60, 72, 80, 90, 96, 100, 108, 120, 144, 150, 160, 180, 200, 216, 240, 270, 288, 300, 360, 400, 432, 450, 480, 540, 600, 720, 800, 864, 900, 1080, 1200, 1350, 1440, 1800, 2160, 2400, 2700, 3600, 4320, 5400, 7200, 10800, 21600.
Hence, product of even factors of 21600 is; 2 x 4 x 6 x 8 x 10 x 12 x 16 x 18 x 20 x 24 x 30 x 32 x 36 x 40 x 48 x 50 x 54 x 60 x 72 x 80 x 90 x 96 x 100 x 108 x 120 x 144 x 150 x 160 x 180 x 200 x 216 x 240 x 270 x 288 x 300 x 360 x 400 x 432 x 450 x 480 x 540 x 600 x 720 x 800 x 864 x 900 x 1080 x 1200 x 1350 x 1440 x 1800 x 2160 x 2400 x 2700 x 3600 x 4320 x 5400 x 7200 x 10800 x 21600 = 1.1601453520892987e+139.

Joy wants to calculate mean of all the factors of 21600. Help him in finding the mean of 21600.

Factors of 21600 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 27, 30, 32, 36, 40, 45, 48, 50, 54, 60, 72, 75, 80, 90, 96, 100, 108, 120, 135, 144, 150, 160, 180, 200, 216, 225, 240, 270, 288, 300, 360, 400, 432, 450, 480, 540, 600, 675, 720, 800, 864, 900, 1080, 1200, 1350, 1440, 1800, 2160, 2400, 2700, 3600, 4320, 5400, 7200, 10800, 21600.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 21600 is 1 + 2 + 3 + 4 + 5 + 6 + 8 + 9 + 10 + 12 + 15 + 16 + 18 + 20 + 24 + 25 + 27 + 30 + 32 + 36 + 40 + 45 + 48 + 50 + 54 + 60 + 72 + 75 + 80 + 90 + 96 + 100 + 108 + 120 + 135 + 144 + 150 + 160 + 180 + 200 + 216 + 225 + 240 + 270 + 288 + 300 + 360 + 400 + 432 + 450 + 480 + 540 + 600 + 675 + 720 + 800 + 864 + 900 + 1080 + 1200 + 1350 + 1440 + 1800 + 2160 + 2400 + 2700 + 3600 + 4320 + 5400 + 7200 + 10800 + 21600 = 78120.
Hence, the mean of factors of 21600 is 78120 ÷ 72 = 1085.00.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 21600? 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, 32, 36, 40, 45, 48, 50, 54, 60, 72, 75, 80, 90, 96, 100, 108, 120, 135, 144, 150, 160, 180, 200, 216, 225, 240, 270, 288, 300, 360, 400, 432, 450, 480, 540, 600, 675, 720, 800, 864, 900, 1080, 1200, 1350, 1440, 1800, 2160, 2400, 2700, 3600, 4320, 5400, 7200, 10800, 21600.
Negative factors are -1, -2, -3, -4, -5, -6, -8, -9, -10, -12, -15, -16, -18, -20, -24, -25, -27, -30, -32, -36, -40, -45, -48, -50, -54, -60, -72, -75, -80, -90, -96, -100, -108, -120, -135, -144, -150, -160, -180, -200, -216, -225, -240, -270, -288, -300, -360, -400, -432, -450, -480, -540, -600, -675, -720, -800, -864, -900, -1080, -1200, -1350, -1440, -1800, -2160, -2400, -2700, -3600, -4320, -5400, -7200, -10800, -21600.

How many factors are there for 21600?

Joey wants to write all the prime factors of 21600 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 21600 are 2, 2, 2, 2, 2, 3, 3, 3, 5, 5.
So in exponential form it can be written as 2⁵ x 3³ x 5².

Kevin has been asked to write 71 factor(s) of 21600. Can you predict the answer?

71 factor(s) of 21600 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 27, 30, 32, 36, 40, 45, 48, 50, 54, 60, 72, 75, 80, 90, 96, 100, 108, 120, 135, 144, 150, 160, 180, 200, 216, 225, 240, 270, 288, 300, 360, 400, 432, 450, 480, 540, 600, 675, 720, 800, 864, 900, 1080, 1200, 1350, 1440, 1800, 2160, 2400, 2700, 3600, 4320, 5400, 7200, 10800.