Factors of 1200

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Factors of 1200 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 40, 48, 50, 60, 75, 80, 100, 120, 150, 200, 240, 300, 400, 600, and 1200

How to find factors of a number

1. Steps to find factors of 1200 using Division Method

Find all the numbers which can divide 1200 without leaving any remainder, starting from number 1 upto 600 (half of 1200). The number 1 and the number (1200) itself are always factors of the given number (1200).
Note down all such number. All of those numbers are factors of 1200.

Example: Find factors of 1200

Divide 1200 by 1: 1200 ÷ 1 : Remainder = 0
Divide 1200 by 2: 1200 ÷ 2 : Remainder = 0
Divide 1200 by 3: 1200 ÷ 3 : Remainder = 0
Divide 1200 by 4: 1200 ÷ 4 : Remainder = 0
Divide 1200 by 5: 1200 ÷ 5 : Remainder = 0
Divide 1200 by 6: 1200 ÷ 6 : Remainder = 0
Divide 1200 by 8: 1200 ÷ 8 : Remainder = 0
Divide 1200 by 10: 1200 ÷ 10 : Remainder = 0
Divide 1200 by 12: 1200 ÷ 12 : Remainder = 0
Divide 1200 by 15: 1200 ÷ 15 : Remainder = 0
Divide 1200 by 16: 1200 ÷ 16 : Remainder = 0
Divide 1200 by 20: 1200 ÷ 20 : Remainder = 0
Divide 1200 by 24: 1200 ÷ 24 : Remainder = 0
Divide 1200 by 25: 1200 ÷ 25 : Remainder = 0
Divide 1200 by 30: 1200 ÷ 30 : Remainder = 0
Divide 1200 by 40: 1200 ÷ 40 : Remainder = 0
Divide 1200 by 48: 1200 ÷ 48 : Remainder = 0
Divide 1200 by 50: 1200 ÷ 50 : Remainder = 0
Divide 1200 by 60: 1200 ÷ 60 : Remainder = 0
Divide 1200 by 75: 1200 ÷ 75 : Remainder = 0
Divide 1200 by 80: 1200 ÷ 80 : Remainder = 0
Divide 1200 by 100: 1200 ÷ 100 : Remainder = 0
Divide 1200 by 120: 1200 ÷ 120 : Remainder = 0
Divide 1200 by 150: 1200 ÷ 150 : Remainder = 0
Divide 1200 by 200: 1200 ÷ 200 : Remainder = 0
Divide 1200 by 240: 1200 ÷ 240 : Remainder = 0
Divide 1200 by 300: 1200 ÷ 300 : Remainder = 0
Divide 1200 by 400: 1200 ÷ 400 : Remainder = 0
Divide 1200 by 600: 1200 ÷ 600 : Remainder = 0
Divide 1200 by 1200: 1200 ÷ 1200 : Remainder = 0

Hence, Factors of 1200 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 40, 48, 50, 60, 75, 80, 100, 120, 150, 200, 240, 300, 400, 600, and 1200

2. Steps to find factors of 1200 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 1200 using the division method, follow these steps:

Step 1. Start dividing 1200 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 1200, which is 2. Divide 1200 by 2 to obtain the quotient (600).
1200 ÷ 2 = 600
Step 3. Repeat step 1 with the obtained quotient (600).
600 ÷ 2 = 300

300 ÷ 2 = 150

150 ÷ 2 = 75

75 ÷ 3 = 25

25 ÷ 5 = 5

5 ÷ 5 = 1

So, the prime factorization of 1200 is, 1200 = 2 x 2 x 2 x 2 x 3 x 5 x 5.

Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 1200 as shown below:

So, the prime factorization of 1200 is, 1200 = 2 x 2 x 2 x 2 x 3 x 5 x 5.

3. Find factors of 1200 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 1200 would be the two numbers which, when multiplied, give 1200 as the result.

The following table represents the calculation of factors of 1200 in pairs:

Factor Pair	Pair Factorization
1 and 1200	1 x 1200 = 1200
2 and 600	2 x 600 = 1200
3 and 400	3 x 400 = 1200
4 and 300	4 x 300 = 1200
5 and 240	5 x 240 = 1200
6 and 200	6 x 200 = 1200
8 and 150	8 x 150 = 1200
10 and 120	10 x 120 = 1200
12 and 100	12 x 100 = 1200
15 and 80	15 x 80 = 1200
16 and 75	16 x 75 = 1200
20 and 60	20 x 60 = 1200
24 and 50	24 x 50 = 1200
25 and 48	25 x 48 = 1200
30 and 40	30 x 40 = 1200

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 1200. They are called negative pair factors.

Hence, the negative pairs of 1200 would be ( -1 , -1200 ) , ( -2 , -600 ) , ( -3 , -400 ) , ( -4 , -300 ) , ( -5 , -240 ) , ( -6 , -200 ) , ( -8 , -150 ) , ( -10 , -120 ) , ( -12 , -100 ) , ( -15 , -80 ) , ( -16 , -75 ) , ( -20 , -60 ) , ( -24 , -50 ) , ( -25 , -48 ) and ( -30 , -40 ) .

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. 1200 is a factor of itself.
1 is a factor of every number. Eg. 1 is a factor of 1200.
Every number is a factor of zero (0), since 1200 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, 10, 12, 15, 16, 20, 24, 25, 30, 40, 48, 50, 60, 75, 80, 100, 120, 150, 200, 240, 300, 400, 600, 1200 are exact divisors of 1200.
Factors of 1200 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 40, 48, 50, 60, 75, 80, 100, 120, 150, 200, 240, 300, 400, 600, 1200. Each factor divides 1200 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, 10, 12, 15, 16, 20, 24, 25, 30, 40, 48, 50, 60, 75, 80, 100, 120, 150, 200, 240, 300, 400, 600, 1200 are all less than or equal to 1200.

Frequently Asked Questions

What are the prime factors of 1200?
The factors of 1200 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 40, 48, 50, 60, 75, 80, 100, 120, 150, 200, 240, 300, 400, 600, 1200.
Prime factors of 1200 are 2, 2, 2, 2, 3, 5, 5.
What two numbers make 1200?
Two numbers that make 1200 are 2 and 600.
What is the greatest prime factors of 1200?
The greatest prime factor of 1200 is 5.
What are factors of 1200?
Factors of 1200 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 40, 48, 50, 60, 75, 80, 100, 120, 150, 200, 240, 300, 400, 600, 1200.
How do you find factors of a negative number? ( eg. -1200 )?
Factors of -1200 are -1, -2, -3, -4, -5, -6, -8, -10, -12, -15, -16, -20, -24, -25, -30, -40, -48, -50, -60, -75, -80, -100, -120, -150, -200, -240, -300, -400, -600, -1200.
What are five multiples of 1200?
First five multiples of 1200 are 2400, 3600, 4800, 6000, 7200.
Write some multiples of 1200?
First five multiples of 1200 are 2400, 3600, 4800, 6000.
Is 1200 a perfect square?
No 1200 is not a perfect square.
What two numbers make 1200?
Two numbers that make 1200 are 2 and 600.

Examples of Factors

What is prime factorization of 1200?

Prime factorization of 1200 is 2 x 2 x 2 x 2 x 3 x 5 x 5 = 2⁴ x 3 x 5².

Sammy is puzzled while calculating the prime factors of 1200. Can you help him find them?

Factors of 1200 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 40, 48, 50, 60, 75, 80, 100, 120, 150, 200, 240, 300, 400, 600, 1200.
Prime factors of 1200 are 2, 2, 2, 2, 3, 5, 5

Kevin has been asked to write 29 factor(s) of 1200. Can you predict the answer?

29 factor(s) of 1200 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 40, 48, 50, 60, 75, 80, 100, 120, 150, 200, 240, 300, 400, 600.

Joey wants to write all the prime factors of 1200 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 1200 are 2, 2, 2, 2, 3, 5, 5.
So in exponential form it can be written as 2⁴ x 3 x 5².

How many factors are there for 1200?

Factors of 1200 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 40, 48, 50, 60, 75, 80, 100, 120, 150, 200, 240, 300, 400, 600, 1200.
So there are in total 30 factors.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 1200? Help her in writing all the factors.

Positive factors are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 40, 48, 50, 60, 75, 80, 100, 120, 150, 200, 240, 300, 400, 600, 1200.
Negative factors are -1, -2, -3, -4, -5, -6, -8, -10, -12, -15, -16, -20, -24, -25, -30, -40, -48, -50, -60, -75, -80, -100, -120, -150, -200, -240, -300, -400, -600, -1200.

Can you help Rubel to find out the product of the even factors of 1200?

Factors of 1200 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 40, 48, 50, 60, 75, 80, 100, 120, 150, 200, 240, 300, 400, 600, 1200.
Even factors of 1200 are 2, 4, 6, 8, 10, 12, 16, 20, 24, 30, 40, 48, 50, 60, 80, 100, 120, 150, 200, 240, 300, 400, 600, 1200.
Hence, product of even factors of 1200 is; 2 x 4 x 6 x 8 x 10 x 12 x 16 x 20 x 24 x 30 x 40 x 48 x 50 x 60 x 80 x 100 x 120 x 150 x 200 x 240 x 300 x 400 x 600 x 1200 = 3.6520347436056576e+40.