# What are all the factors, the prime factorization, and factor pairs of 31200?

To find the factors of 31200, divide 31200 by each number starting with 1 and working up to 31200

## What is a factor in math ?

Factors are the numbers you multiply together to get another number. For example, the factors of 15 are 3 and 5 because 3 × 5 = 15.

The factors of a number can be positive or negative, but they cannot be zero.

The factors of a number can be used to find out if the number is prime or not.

A prime number is a number that has only two factors: itself and 1. For example, the number 7 is prime because its only factors are 7 and 1.

## List all of the factors of 31200 ?

To calculate the factors of 31200 , you can use the division method.

1. Begin by dividing 31200 by the smallest possible number, which is 2.

2. If the division is even, then 2 is a factor of 31200.

3. Continue dividing 31200 by larger numbers until you find an odd number that does not divide evenly into 31200 .

4. The numbers that divide evenly into 31200 are the factors of 31200 .

Now let us find how to calculate all the factors of Thirty-one thousand two hundred :

31200 ÷ 1 = 31200
31200 ÷ 2 = 15600
31200 ÷ 3 = 10400
31200 ÷ 4 = 7800
31200 ÷ 5 = 6240
31200 ÷ 6 = 5200
31200 ÷ 8 = 3900
31200 ÷ 10 = 3120
31200 ÷ 12 = 2600
31200 ÷ 13 = 2400
31200 ÷ 15 = 2080
31200 ÷ 16 = 1950
31200 ÷ 20 = 1560
31200 ÷ 24 = 1300
31200 ÷ 25 = 1248
31200 ÷ 26 = 1200
31200 ÷ 30 = 1040
31200 ÷ 32 = 975
31200 ÷ 39 = 800
31200 ÷ 40 = 780
31200 ÷ 48 = 650
31200 ÷ 50 = 624
31200 ÷ 52 = 600
31200 ÷ 60 = 520
31200 ÷ 65 = 480
31200 ÷ 75 = 416
31200 ÷ 78 = 400
31200 ÷ 80 = 390
31200 ÷ 96 = 325
31200 ÷ 100 = 312
31200 ÷ 104 = 300
31200 ÷ 120 = 260
31200 ÷ 130 = 240
31200 ÷ 150 = 208
31200 ÷ 156 = 200
31200 ÷ 160 = 195
31200 ÷ 195 = 160
31200 ÷ 200 = 156
31200 ÷ 208 = 150
31200 ÷ 240 = 130
31200 ÷ 260 = 120
31200 ÷ 300 = 104
31200 ÷ 312 = 100
31200 ÷ 325 = 96
31200 ÷ 390 = 80
31200 ÷ 400 = 78
31200 ÷ 416 = 75
31200 ÷ 480 = 65
31200 ÷ 520 = 60
31200 ÷ 600 = 52
31200 ÷ 624 = 50
31200 ÷ 650 = 48
31200 ÷ 780 = 40
31200 ÷ 800 = 39
31200 ÷ 975 = 32
31200 ÷ 1040 = 30
31200 ÷ 1200 = 26
31200 ÷ 1248 = 25
31200 ÷ 1300 = 24
31200 ÷ 1560 = 20
31200 ÷ 1950 = 16
31200 ÷ 2080 = 15
31200 ÷ 2400 = 13
31200 ÷ 2600 = 12
31200 ÷ 3120 = 10
31200 ÷ 3900 = 8
31200 ÷ 5200 = 6
31200 ÷ 6240 = 5
31200 ÷ 7800 = 4
31200 ÷ 10400 = 3
31200 ÷ 15600 = 2
31200 ÷ 31200 = 1

As you can see, the factors of 31200 are 1 , 2 , 3 , 4 , 5 , 6 , 8 , 10 , 12 , 13 , 15 , 16 , 20 , 24 , 25 , 26 , 30 , 32 , 39 , 40 , 48 , 50 , 52 , 60 , 65 , 75 , 78 , 80 , 96 , 100 , 104 , 120 , 130 , 150 , 156 , 160 , 195 , 200 , 208 , 240 , 260 , 300 , 312 , 325 , 390 , 400 , 416 , 480 , 520 , 600 , 624 , 650 , 780 , 800 , 975 , 1040 , 1200 , 1248 , 1300 , 1560 , 1950 , 2080 , 2400 , 2600 , 3120 , 3900 , 5200 , 6240 , 7800 , 10400 , 15600 and 31200 .

## How many factors of 31200 are there ?

The factors of 31200 are the numbers that can evenly divide 31200 . These numbers are 1 , 2 , 3 , 4 , 5 , 6 , 8 , 10 , 12 , 13 , 15 , 16 , 20 , 24 , 25 , 26 , 30 , 32 , 39 , 40 , 48 , 50 , 52 , 60 , 65 , 75 , 78 , 80 , 96 , 100 , 104 , 120 , 130 , 150 , 156 , 160 , 195 , 200 , 208 , 240 , 260 , 300 , 312 , 325 , 390 , 400 , 416 , 480 , 520 , 600 , 624 , 650 , 780 , 800 , 975 , 1040 , 1200 , 1248 , 1300 , 1560 , 1950 , 2080 , 2400 , 2600 , 3120 , 3900 , 5200 , 6240 , 7800 , 10400 , 15600 and 31200.

Thus, there are a total of 72 factors of 31200

## What are the factor pairs of 31200 ?

Factor Pairs of 31200 are combinations of two factors that when multiplied together equal 31200. There are many ways to calculate the factor pairs of 31200 .

One easy way is to list out the factors of 31200 :
1 , 2 , 3 , 4 , 5 , 6 , 8 , 10 , 12 , 13 , 15 , 16 , 20 , 24 , 25 , 26 , 30 , 32 , 39 , 40 , 48 , 50 , 52 , 60 , 65 , 75 , 78 , 80 , 96 , 100 , 104 , 120 , 130 , 150 , 156 , 160 , 195 , 200 , 208 , 240 , 260 , 300 , 312 , 325 , 390 , 400 , 416 , 480 , 520 , 600 , 624 , 650 , 780 , 800 , 975 , 1040 , 1200 , 1248 , 1300 , 1560 , 1950 , 2080 , 2400 , 2600 , 3120 , 3900 , 5200 , 6240 , 7800 , 10400 , 15600 , 31200

Then, pair up the factors:
(1,31200),(2,15600),(3,10400),(4,7800),(5,6240),(6,5200),(8,3900),(10,3120),(12,2600),(13,2400),(15,2080),(16,1950),(20,1560),(24,1300),(25,1248),(26,1200),(30,1040),(32,975),(39,800),(40,780),(48,650),(50,624),(52,600),(60,520),(65,480),(75,416),(78,400),(80,390),(96,325),(100,312),(104,300),(120,260),(130,240),(150,208),(156,200) and (160,195) These are the factor pairs of 31200 .

## Prime Factorisation of 31200

There are a few different methods that can be used to calculate the prime factorization of a number. Two of the most common methods are listed below.

1) Use a factor tree :

1. Take the number you want to find the prime factorization of and write it at the top of the page

2. Find the smallest number that goes into the number you are finding the prime factorization of evenly and write it next to the number you are finding the prime factorization of

3. Draw a line under the number you just wrote and the number you are finding the prime factorization of

4. Repeat step 2 with the number you just wrote until that number can no longer be divided evenly

5. The numbers written on the lines will be the prime factors of the number you started with

For example, to calculate the prime factorization of 31200 using a factor tree, we would start by writing 31200 on a piece of paper. Then, we would draw a line under it and begin finding factors.

The final prime factorization of 31200 would be 2 x 2 x 2 x 2 x 2 x 3 x 5 x 5 x 13.

2) Use a factorization method :

There are a few different factorization methods that can be used to calculate the prime factorization of a number.

One common method is to start by dividing the number by the smallest prime number that will divide evenly into it.

Then, continue dividing the number by successively larger prime numbers until the number has been fully factorised.

For example, to calculate the prime factorization of 31200 using this method, we keep dividing until it gives a non-zero remainder.

31200 ÷ 2 = 15600
15600 ÷ 2 = 7800
7800 ÷ 2 = 3900
3900 ÷ 2 = 1950
1950 ÷ 2 = 975
975 ÷ 3 = 325
325 ÷ 5 = 65
65 ÷ 5 = 13
13 ÷ 13 = 1

So the prime factors of 31200 are 2 x 2 x 2 x 2 x 2 x 3 x 5 x 5 x 13.

## Frequently Asked Questions on Factors

### What are all the factors of 31200 ?

The factors of 31200 are 1 , 2 , 3 , 4 , 5 , 6 , 8 , 10 , 12 , 13 , 15 , 16 , 20 , 24 , 25 , 26 , 30 , 32 , 39 , 40 , 48 , 50 , 52 , 60 , 65 , 75 , 78 , 80 , 96 , 100 , 104 , 120 , 130 , 150 , 156 , 160 , 195 , 200 , 208 , 240 , 260 , 300 , 312 , 325 , 390 , 400 , 416 , 480 , 520 , 600 , 624 , 650 , 780 , 800 , 975 , 1040 , 1200 , 1248 , 1300 , 1560 , 1950 , 2080 , 2400 , 2600 , 3120 , 3900 , 5200 , 6240 , 7800 , 10400 , 15600 and 31200.

### What is the prime factorization of 31200 ?

The prime factorization of 31200 is 2 x 2 x 2 x 2 x 2 x 3 x 5 x 5 x 13 or 25 x 31 x 52 x 131, where 2 , 3 , 5 , 13 are the prime numbers .

### What are the prime factors of 31200 ?

The prime factors of 31200 are 2 , 3 , 5 , 13 .

### Is 31200 a prime number ?

A prime number is a number that has only two factors 1 and itself.
31200 it is not a prime number because it has the factors 1 , 2 , 3 , 4 , 5 , 6 , 8 , 10 , 12 , 13 , 15 , 16 , 20 , 24 , 25 , 26 , 30 , 32 , 39 , 40 , 48 , 50 , 52 , 60 , 65 , 75 , 78 , 80 , 96 , 100 , 104 , 120 , 130 , 150 , 156 , 160 , 195 , 200 , 208 , 240 , 260 , 300 , 312 , 325 , 390 , 400 , 416 , 480 , 520 , 600 , 624 , 650 , 780 , 800 , 975 , 1040 , 1200 , 1248 , 1300 , 1560 , 1950 , 2080 , 2400 , 2600 , 3120 , 3900 , 5200 , 6240 , 7800 , 10400 , 15600 and 31200.