# Factors of 72

What are the Factors of 72?

First thing first, a Factor is a number that divides a number at one go without producing any remainder. For example, if we multiply 2 with 3, the result will be 6. So if we divide 6 by 3 we will get 2 and if we divide 6 by 3 we will get 2. This means that 2 and 3 are the factors of 6. Now, what are the factors of 72? Well, Factors of 72 are the numbers, that when multiplied together in a pair of two return the result as 72. Therefore, 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72 are the factors of 72.

How to Find the Factors of 72?

In order to see what are the true factors of 72, we will divide 72 by all the numbers starting from 1 to 72.

 721= 72 7211= 6.5 7221= 3.42 7231= 232 72 2= 36 7212= 6 7222= 3.27 7232= 225 723= 24 7213= 5.53 7223= 3.13 7233= 218 724= 14 7214= 5.14 7224= 3 7234= 211 725= 14.4 7215= 4.8 7225= 2.88 7235= 2.05 726= 12 7216= 4.5 7226= 2.7 7236= 2 727= 10.2 7217= 4.2 7227= 2.6 7237= 1.9 728= 9 7218= 4 7228= 2.5 7238= 1.8 729= 8 7219= 3.7 7229= 2.48 7239= 1.8 7210= 7.2 7220= 3.6 7230= 2.4 7240= 1.8

 7241= 1.7 7251= 1.41 7261= 1.18 7271= 1.01 7242= 1.71 7252= 1.38 7262= 1.16 7272= 1 7243= 1.67 7253= 1.35 7263= 1.14 7244= 1.63 7254= 1.33 7264= 1.12 7245= 1.6 7255= 1.30 7265= 1.10 7246= 1.56 7256= 1.28 7266= 1.09 7247= 1.53 7257= 1.26 7267= 1.07 7248= 1.5 7258= 1.24 7268= 1.05 7249=1.46 7259= 1.22 7269= 1.04 7250=1.44 72 60= 1.2 7270= 1.02

Therefore, we conclude that the factors we stated were true and were the only factors of 72. So there are all total of 12 factors of 72.

Pair Factors of 72

Pair factors are the combinations of any two factors that are multiplied together to give 72 as the product. Here we can see all the Positive pair factors of 72.

 1 x 72= 72 therefore, 1 and 72 are a factor pair of 72 2 x 36= 72 therefore, 2 and 36 are a factor pair of 72 3 x 24= 72 therefore, 3 and 24 are a factor pair of 72 4 x 18= 72 therefore, 4 and 18 are a factor pair of 72 6 x 12= 72 therefore, 6 and 12 are a factor pair of 72 8 x 9= 72 therefore, 8 and 9 are a factor pair of 72 9 x 8= 72 therefore, 9 and 8 are a factor pair of 72 12 x 6= 72 therefore, 12 and 6 are a factor pair of 72 18 x 4= 72 therefore, 18 and 4 are a factor pair of 72 24 x 3= 72 therefore, 24 and 3 are a factor pair of 72 36 x 2= 72 therefore, 36 and 2 are a factor pair of 72 72 x 1= 72 therefore, 72 and 1 are a factor pair of 72

Solved Examples

Example 1) Find the factors of the following numbers:

i) 87

ii) 162

iii) 52

iv) 72

v) 198

Solution 1) let us find the factors of the following numbers:

i) Factors of 87 are:

 3 87 29 29 1

ii) Factors of 162 are:

 2 162 3 81 3 27 3 9 3 3 1

iii) Factors of 52 are:

 2 52 2 26 13 13 1

iv) Factors of 72 are:

 2 72 2 36 2 18 3 9 3 3 1

v) Factors of 198 are:

 2 198 3 99 3 33 11 11 1

Example 2) Find the Factors of the Following:

i) 124

ii) 72

iii) 66

iv) 57

v) 180

Solution 2) Finding the factors of the following numbers:

i) The factors of 124 are:

 2 124 2 62 31 31 1

ii) Factors of 72 are:

 2 72 2 36 2 18 3 9 3 3 1

iii) Factors of 66 are:

 3 66 2 22 11 11 1

iv) Factors of 57 are:

 3 57 19 19 1

v) Factors of 180 are:

 2 180 2 90 5 45 7 7 1

Question 1. What is the Difference Between a Factor, a Prime Factor, and a Multiple?

Answer. A Factor is a number that we can further break it down. It is all the number that can be multiplied to give the original number, but a prime factor cannot be broken down.

For example, the factors of 30 are 1, 2, 3, 5, 6, 10, 15, and 30. But the prime factors of 30 are 2, 3, and 5.

Now, coming to factors and multiples, they are very different from each other yet it is very confusing to remember what is what?!! Well, let us clarify it now, a factor is an exact divisor of a number whereas a multiple is the result we get after the multiplication is done.

Question 2. What are the First 20 Multiples of 72?

Answer. We can find the first 20 multiples of 72 by multiplying 72 with numbers starting from 1 to 20. So let us find out the first 20 multiples of 72:

72 x 1 = 72

72 x 2 = 144

72 x 3 = 216

72 x 4 = 288

72 x 5 = 360

72 x 6 = 432

72 x 7 = 504

72 x 8 = 576

72 x 9 = 648

72 x 10 = 720

72 x 11 = 792

72 x 12 = 864

72 x 13 = 936

72 x 14 = 1008

72 x 15 = 1080

72 x 16 = 1152

72 x 17 = 1224

72 x 18 = 1296

72 x 19 = 1368

72 x 20 = 1440