[Maths Class Notes] on Factors of 72 Pdf for Exam

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.

72 ÷ 1 = 72	72 ÷ 11 = 6.5	72 ÷ 21 = 3.42	72 ÷ 31 = 232
72 ÷ 2 = 36	72 ÷ 12 = 6	72 ÷ 22 = 3.27	72 ÷ 32 = 225
72 ÷ 3 = 24	72 ÷ 13 = 5.53	72 ÷ 23 = 3.13	72 ÷ 33 = 218
72 ÷ 4 = 14	72 ÷ 14 = 5.14	72 ÷ 24 = 3	72 ÷ 34 = 211
72 ÷ 5 = 14.4	72 ÷ 15 = 4.8	72 ÷ 25 = 2.88	72 ÷ 35 = 2.05
72 ÷ 6 = 12	72 ÷ 16 = 4.5	72 ÷ 26 = 2.7	72 ÷ 36 = 2
72 ÷ 7 = 10.2	72 ÷ 17 = 4.2	72 ÷ 27 = 2.6	72 ÷ 37 = 1.9
72 ÷ 8 = 9	72 ÷ 18 = 4	72 ÷ 28 = 2.5	72 ÷ 38 = 1.8
72 ÷ 9 = 8	72 ÷ 19 = 3.7	72 ÷ 29 = 2.48	72 ÷ 39 = 1.8
72 ÷ 10 = 7.2	72 ÷ 20 = 3.6	72 ÷ 30 = 2.4	72 ÷ 40 = 1.8

72 ÷ 41 = 1.7	72 ÷ 51 = 1.41	72 ÷ 61 = 1.18	72 ÷ 71 = 1.01
72 ÷ 42 = 1.71	72 ÷ 52 = 1.38	72 ÷ 62 = 1.16	72 ÷ 72 = 1
72 ÷ 43 = 1.67	72 ÷ 53 = 1.35	72 ÷ 63 = 1.14
72 ÷ 44 = 1.63	72 ÷ 54= 1.33	72 ÷ 64 = 1.12
72 ÷ 45 = 1.6	72 ÷ 55 = 1.30	72 ÷ 65 = 1.10
72 ÷ 46 = 1.56	72 ÷ 56 = 1.28	72 ÷ 66 = 1.09
72 ÷ 47 = 1.53	72 ÷ 57 = 1.26	72 ÷ 67 = 1.07
72 ÷ 48 = 1.5	72 ÷ 58 = 1.24	72 ÷ 68 = 1.05
72 ÷ 49 =1.46	72 ÷ 59 = 1.22	72 ÷ 69 = 1.04
72 ÷ 50 =1.44	72 ÷ 60 = 1.2	72 ÷ 70 = 1.02

Therefore, we conclude that the Factors we stated were true and were the only Factors of 72. So there are a 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 [times] 72 = 72	therefore, 1 and 72 are a Factor pair of 72
2 [times] 36 = 72	therefore, 2 and 36 are a Factor pair of 72
3 [times] 24 = 72	therefore, 3 and 24 are a Factor pair of 72
4 [times] 18 = 72	therefore, 4 and 18 are a Factor pair of 72
6 [times] 12 = 72	therefore, 6 and 12 are a Factor pair of 72
8 [times] 9 = 72	therefore, 8 and 9 are a Factor pair of 72
9 [times] 8 = 72	therefore, 9 and 8 are a Factor pair of 72
12 [times] 6 = 72	therefore, 12 and 6 are a Factor pair of 72
18 [times] 4 = 72	therefore, 18 and 4 are a Factor pair of 72
24 [times] 3 = 72	therefore, 24 and 3 are a Factor pair of 72
36 [times] 2 = 72	therefore, 36 and 2 are a Factor pair of 72
72 [times] 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:

ii) Factors of 162 are:

iii) Factors of 52 are:

iv) Factors of 72 are:

v) Factors of 198 are:

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:

ii) Factors of 72 are:

iii) Factors of 66 are:

iv) Factors of 57 are:

v) Factors of 180 are:

What are the various methods of Calculating Factors of 72?

There are two methods to calculate the Factors of 72. Both these methods are quite easy to understand. Here is a quick overview of these Factorisation methods:

Division Method: For calculating the Factors of 72 by division method, you have to use the Numbers that can divide 72 without leaving a remainder. Here are the Factors of 72 as per the division method:

72 ÷ 1 = 72
72 ÷ 2 = 36
72 ÷ 3 = 24
72 ÷ 4 = 18
72 ÷ 6 = 12
72 ÷ 8 = 9
72 ÷ 9 = 8
72 ÷ 12 = 6
72 ÷ 18 = 4
72 ÷ 24 = 3
72 ÷ 36 = 2
72 ÷ 72 = 1

Prime Factorisation Method: In this method, you have to express 72 as a product of its prime Factors. Start by dividing 72 with the smallest prime Number i.e. 2, which gives you 36. Then divide 72 by 3 to obtain 36. And keep doing so until you receive 1 as your quotient. So the prime Factors of 72 are 2 [times] 2 [times] 2 [times] 3 [times] 3.

Tips to Find the Factors of 72 – Pair Factors and Solved Examples

Factors and multiples are important concepts of Mathematics. That is why you must know the best ways to solve the questions related to these topics. Here are some tips and tricks to find the Factors of 72 and other Numbers as well:

Whether you choose the division method or the prime Factorisation method, make sure to follow the right sequence of steps to obtain the correct answer.
Gain a good understanding of the formulas or concepts used to find the Factors of 72 and other Numbers.
Once you understand how to find the Factors of 72, you will be able to calculate the Factors of any given Number.
By practising more questions related to the Factors of 72, you can become more efficient and strengthen your grasp of the concept.
Once you are done finding the Factors of 72, cross-check your answer to check whether you have understood the topic or not.
If you have made any mistakes in your calculation, try to rectify them as soon as possible. It will help you avoid silly mistakes in your exams and secure excellent marks.
You can try different questions from other reference books to test your knowledge and see whether you have understood the topic or not.
Have a firm grip on both the methods to calculate Factors of a Number by practising more questions.

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