# What are all the factors, the prime factorization, and factor pairs of 20400?

To find the factors of 20400, divide 20400 by each number starting with 1 and working up to 20400

## 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 20400 ?

To calculate the factors of 20400 , you can use the division method.

1. Begin by dividing 20400 by the smallest possible number, which is 2.

2. If the division is even, then 2 is a factor of 20400.

3. Continue dividing 20400 by larger numbers until you find an odd number that does not divide evenly into 20400 .

4. The numbers that divide evenly into 20400 are the factors of 20400 .

Now let us find how to calculate all the factors of Twenty thousand four hundred :

20400 ÷ 1 = 20400
20400 ÷ 2 = 10200
20400 ÷ 3 = 6800
20400 ÷ 4 = 5100
20400 ÷ 5 = 4080
20400 ÷ 6 = 3400
20400 ÷ 8 = 2550
20400 ÷ 10 = 2040
20400 ÷ 12 = 1700
20400 ÷ 15 = 1360
20400 ÷ 16 = 1275
20400 ÷ 17 = 1200
20400 ÷ 20 = 1020
20400 ÷ 24 = 850
20400 ÷ 25 = 816
20400 ÷ 30 = 680
20400 ÷ 34 = 600
20400 ÷ 40 = 510
20400 ÷ 48 = 425
20400 ÷ 50 = 408
20400 ÷ 51 = 400
20400 ÷ 60 = 340
20400 ÷ 68 = 300
20400 ÷ 75 = 272
20400 ÷ 80 = 255
20400 ÷ 85 = 240
20400 ÷ 100 = 204
20400 ÷ 102 = 200
20400 ÷ 120 = 170
20400 ÷ 136 = 150
20400 ÷ 150 = 136
20400 ÷ 170 = 120
20400 ÷ 200 = 102
20400 ÷ 204 = 100
20400 ÷ 240 = 85
20400 ÷ 255 = 80
20400 ÷ 272 = 75
20400 ÷ 300 = 68
20400 ÷ 340 = 60
20400 ÷ 400 = 51
20400 ÷ 408 = 50
20400 ÷ 425 = 48
20400 ÷ 510 = 40
20400 ÷ 600 = 34
20400 ÷ 680 = 30
20400 ÷ 816 = 25
20400 ÷ 850 = 24
20400 ÷ 1020 = 20
20400 ÷ 1200 = 17
20400 ÷ 1275 = 16
20400 ÷ 1360 = 15
20400 ÷ 1700 = 12
20400 ÷ 2040 = 10
20400 ÷ 2550 = 8
20400 ÷ 3400 = 6
20400 ÷ 4080 = 5
20400 ÷ 5100 = 4
20400 ÷ 6800 = 3
20400 ÷ 10200 = 2
20400 ÷ 20400 = 1

As you can see, the factors of 20400 are 1 , 2 , 3 , 4 , 5 , 6 , 8 , 10 , 12 , 15 , 16 , 17 , 20 , 24 , 25 , 30 , 34 , 40 , 48 , 50 , 51 , 60 , 68 , 75 , 80 , 85 , 100 , 102 , 120 , 136 , 150 , 170 , 200 , 204 , 240 , 255 , 272 , 300 , 340 , 400 , 408 , 425 , 510 , 600 , 680 , 816 , 850 , 1020 , 1200 , 1275 , 1360 , 1700 , 2040 , 2550 , 3400 , 4080 , 5100 , 6800 , 10200 and 20400 .

## How many factors of 20400 are there ?

The factors of 20400 are the numbers that can evenly divide 20400 . These numbers are 1 , 2 , 3 , 4 , 5 , 6 , 8 , 10 , 12 , 15 , 16 , 17 , 20 , 24 , 25 , 30 , 34 , 40 , 48 , 50 , 51 , 60 , 68 , 75 , 80 , 85 , 100 , 102 , 120 , 136 , 150 , 170 , 200 , 204 , 240 , 255 , 272 , 300 , 340 , 400 , 408 , 425 , 510 , 600 , 680 , 816 , 850 , 1020 , 1200 , 1275 , 1360 , 1700 , 2040 , 2550 , 3400 , 4080 , 5100 , 6800 , 10200 and 20400.

Thus, there are a total of 60 factors of 20400

## What are the factor pairs of 20400 ?

Factor Pairs of 20400 are combinations of two factors that when multiplied together equal 20400. There are many ways to calculate the factor pairs of 20400 .

One easy way is to list out the factors of 20400 :
1 , 2 , 3 , 4 , 5 , 6 , 8 , 10 , 12 , 15 , 16 , 17 , 20 , 24 , 25 , 30 , 34 , 40 , 48 , 50 , 51 , 60 , 68 , 75 , 80 , 85 , 100 , 102 , 120 , 136 , 150 , 170 , 200 , 204 , 240 , 255 , 272 , 300 , 340 , 400 , 408 , 425 , 510 , 600 , 680 , 816 , 850 , 1020 , 1200 , 1275 , 1360 , 1700 , 2040 , 2550 , 3400 , 4080 , 5100 , 6800 , 10200 , 20400

Then, pair up the factors:
(1,20400),(2,10200),(3,6800),(4,5100),(5,4080),(6,3400),(8,2550),(10,2040),(12,1700),(15,1360),(16,1275),(17,1200),(20,1020),(24,850),(25,816),(30,680),(34,600),(40,510),(48,425),(50,408),(51,400),(60,340),(68,300),(75,272),(80,255),(85,240),(100,204),(102,200),(120,170) and (136,150) These are the factor pairs of 20400 .

## Prime Factorisation of 20400

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 20400 using a factor tree, we would start by writing 20400 on a piece of paper. Then, we would draw a line under it and begin finding factors.

The final prime factorization of 20400 would be 2 x 2 x 2 x 2 x 3 x 5 x 5 x 17.

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 20400 using this method, we keep dividing until it gives a non-zero remainder.

20400 ÷ 2 = 10200
10200 ÷ 2 = 5100
5100 ÷ 2 = 2550
2550 ÷ 2 = 1275
1275 ÷ 3 = 425
425 ÷ 5 = 85
85 ÷ 5 = 17
17 ÷ 17 = 1

So the prime factors of 20400 are 2 x 2 x 2 x 2 x 3 x 5 x 5 x 17.

## Frequently Asked Questions on Factors

### What are all the factors of 20400 ?

The factors of 20400 are 1 , 2 , 3 , 4 , 5 , 6 , 8 , 10 , 12 , 15 , 16 , 17 , 20 , 24 , 25 , 30 , 34 , 40 , 48 , 50 , 51 , 60 , 68 , 75 , 80 , 85 , 100 , 102 , 120 , 136 , 150 , 170 , 200 , 204 , 240 , 255 , 272 , 300 , 340 , 400 , 408 , 425 , 510 , 600 , 680 , 816 , 850 , 1020 , 1200 , 1275 , 1360 , 1700 , 2040 , 2550 , 3400 , 4080 , 5100 , 6800 , 10200 and 20400.

### What is the prime factorization of 20400 ?

The prime factorization of 20400 is 2 x 2 x 2 x 2 x 3 x 5 x 5 x 17 or 24 x 31 x 52 x 171, where 2 , 3 , 5 , 17 are the prime numbers .

### What are the prime factors of 20400 ?

The prime factors of 20400 are 2 , 3 , 5 , 17 .

### Is 20400 a prime number ?

A prime number is a number that has only two factors 1 and itself.
20400 it is not a prime number because it has the factors 1 , 2 , 3 , 4 , 5 , 6 , 8 , 10 , 12 , 15 , 16 , 17 , 20 , 24 , 25 , 30 , 34 , 40 , 48 , 50 , 51 , 60 , 68 , 75 , 80 , 85 , 100 , 102 , 120 , 136 , 150 , 170 , 200 , 204 , 240 , 255 , 272 , 300 , 340 , 400 , 408 , 425 , 510 , 600 , 680 , 816 , 850 , 1020 , 1200 , 1275 , 1360 , 1700 , 2040 , 2550 , 3400 , 4080 , 5100 , 6800 , 10200 and 20400.