Factors of 72

Factors of 72 are the numbers obtained when the original number divides completely with no remainder. The factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72. Besides this, factors of 72 have positive and negative numbers. You can teach kids to recognize the numbers and solve mathematical problems related to factors of a number easily. To make it interesting, you can conduct math activities for kids to keep their interests alive. Apart from factors of 72, kids must learn prime and pair factors of 72 for an effective learning experience. 

Contents 

• What are the Factors of 72?
• How to Find the Factors of 72?
• Solved Examples on Factors of 72
• Benefits of Learning Factors of 72
• Frequently Asked Questions on Factors of 72

Though the number 72 is a composite number, it consists of factors apart from one and the number itself. Sometimes, little ones might find it challenging to understand and memorize factors of 72. In such cases, you need to make entertaining learning experiences for kids to retain the numbers in their memory for a longer period of time. Kids will enjoy learning concepts through games and activities. Therefore, conducting number games for kids can help them solve mathematical problems with speed and accuracy. 

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What are the Factors of 72?

Factors of 72 are the numbers obtained when the original number is divided completely without leaving the remainder. Therefore, the factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72. Besides this, kids must learn about prime factors of 72 that are 2 x 2 x 2 x 3 x 3 = 2³ x 3². If you multiply two factors of 72, the product obtained is the original number. These pair factors of 72 are (1, 72), (2, 36), (3, 24), (4, 18), (6, 12), and (8, 9). The total sum of factors of 72 is 1 + 2 + 3 + 4 + 6 +8 + 9 +12 + 18 + 24 + 36 + 72 = 195. Besides this, factors of 72 have positive and negative numbers. When two negative factors of 72 are multiplied, it gives a positive result. The negative factors of 72 are (-1, -72), (-2, -36), (-3, -24), (-4, -18), (-6, -12), and (-8, -9). 

How to Find the Factors of 72? 

Once kids recognize factors of 72, they must learn to calculate them using multiplication or division methods. This helps them become familiar with factors of 72 and use them accordingly in solving mathematical problems. For that, kids must learn and memorize 100 times tables to calculate factors of 72 with ease. However, check out the methods to find the factors of 72 given below.  

To calculate the factors of 72, you can multiply pairs of numbers to get the original numbers without leaving the remainder. 

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

Therefore, the factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72.  

Pair Factors of 72

Pair factors of 72 are the numbers obtained when two factors of 72 are multiplied to get the original number 72. Find the pair of factors of 72 given below. 

1 x 72 = 72

2 x 36 = 72

3 x 24 = 72

4 x 18 = 72

6 x 12 = 72 

8 x 9 = 72

9 x 8 = 72

12 x 6 = 72

18 x 4 = 72

24 x 3 = 72

36 x 2 = 72 

72 x 1 = 72

Therefore, the pair factors of 72 are (1, 72), (2, 36), (3, 24), (4, 18), (6, 12), and (8, 9). 

Negative Factors of 72 

Apart from positive factors, it also consists of negative factors. When two negative factors of 72 multiply, it gives a positive result. Check out the method to calculate the negative factor of 72 given below.

-1 x -72 = 72

-2 x -36 = 72

-3 x -24 = 72

-4 x -18 = 72

-6 x -12 = 72 

-8 x -9 = 72

-9 x -8 = 72

-12 x -6 = 72

-18 x -4 = 72

-24 x -3 = 72

-36 x -2 = 72 

-72 x -1 = 72

Therefore, the negative factors of 72 are (-1, -72), (-2, -36), (-3, -24), (-4, -18), (-6, -12), and (-8, -9).

Prime Factors of 72

To calculate the prime factors of 72, you need to take the least prime number two and divide it by the original number. You can continue the steps until you get the quotient 1. The steps to calculate the prime factors of 72 are given below:

Step 1: 72/2 = 36

Step 2: 36/2 = 18

Step 3: 18/2 = 9

Since the prime number 2 is not divisible by 9 without leaving the remainder, you can take the number 3 to calculate the prime factor. 

Step 4: 9/3 = 3

Step 5: 3/3 = 1

Therefore, the prime factors of 72 are 2 x 2 x 2 x 3 x 3 = 2³ x 3²

Check multiplication tables related articles

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Solved Examples on Factors of 72

Some solved examples on factors of 72 for kids are mentioned below:

Example 1: Find out the common factors of 72 and 36. 

Solution: Factors of 72 = 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72.

Factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, and 36.

Therefore, the common factors of 72 and 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36. 

Example 2: Harry got 72 pencils from the stationery store. He gave all the pencils to his 36 classmates. How many pencils did each classmate get?

Solution: Number of pencils = 72 

Number of classmates = 36

Total number of pencils received by each classmate = 72/36 = 2

Therefore, the total number of pencils received by each classmate is 2. 

Benefits of Learning Factors of 72 

The benefits of learning factors of 72 for kids are mentioned below:

• It develops mathematical skills in children
• It enhances the concepts of arithmetic operations in children. 
• It helps children solve and calculate mathematical problems related to factors of 72 easily. 
• It improves academic performance in mathematics and other concepts dealing with factors of 72. 

We hope this article on factors of 72 was useful to you. For more about activities, worksheets and games, explore worksheets for kids, math for kids,  puzzles for kids, kids learning sections at Osmo.

Frequently Asked Questions on Factors of 72