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Factors of 72

Maths

Factors of 72

Last updated date: 25th Apr 2024

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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.

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:

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

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.

FAQs on Factors of 72

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

A Factor is a Number that we can further break down. It is all the Numbers 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.

2. What are the First 20 Multiples of 72?

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 \[\times\] 1 = 72
72 \[\times\] 2 = 144
72 \[\times\] 3 = 216
72 \[\times\] 4 = 288
72 \[\times\] 5 = 360
72 \[\times\] 6 = 432
72 \[\times\] 7 = 504
72 \[\times\] 8 = 576
72 \[\times\] 9 = 648
72 \[\times\] 10 = 720
72 \[\times\] 11 = 792
72 \[\times\] 12 = 864
72 \[\times\] 13 = 936
72 \[\times\] 14 = 1008
72 \[\times\] 15 = 1080
72 \[\times\] 16 = 1152
72 \[\times\] 17 = 1224
72 \[\times\] 18 = 1296
72 \[\times\] 19 = 1368
72 \[\times\] 20 = 1440

3. What is the best way to learn Factors of 72 – Pair Factors and Solved Examples?

The best way to learn the Factors of 72 – Pair Factors and Solved Examples is Vedantu’s online learning platform. You will find detailed explanations of Factors of 72 – Pair Factors and Solved Examples on Vedantu.com and gain a better understanding of the concept. Apart from this, we provide a lot of study material on our website for absolutely free to help students learn more conveniently. You can get access to various concepts of maths such as Limits and Derivatives, Integration, Mensuration, etc. from our website.

4. How will the Factors of 72 – Pair Factors and Solved Examples help me?

The Factors of 72 – Pair Factors and Solved Examples will help you in so many ways. By learning to find the Factors of 72, you can also understand the methods of finding Factors of other Numbers as well. It will give you a clear understanding of the concept and help you solve complicated questions with ease. You can use the solved examples to learn how to solve a question and obtain the Factors of different Numbers. Once you go through the Factors of 72 – Pair Factors and Solved Examples thoroughly, you will be able to solve any question related to it with no mistakes.

5. What is the importance of Factors of 72 – Pair Factors and Solved Examples important?

The Factors of 72 – Pair Factors and Solved Examples are quite important for every student. Learning the basics of Factors will make you more proficient in solving any problem related to it. You can use the mathematical formulas and understand the correct way to find the Factors of 72. Moreover, you can learn more about pair Factors, which is a crucial topic of the Maths syllabus. The solved examples from Vedantu will give you an idea of what type of questions are usually asked in the exams. So, if you go through the Factors of 72 – Pair Factors and Solved Examples, you can score better in exams.