Factors Of 72

Factors of a number often come in pairs, and they can be found using different methods. The factors of 72 are: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36,72.
 

To find factors, kids can use different methods for easier calculations. A few commonly used methods are as follows - 

• Use of Multiplication Method
• Use of Division Method
• Use of Prime Factor and Prime Factorization.

So, here we discuss a detailed explanation of the following methods,
 

In this method, we identify pairs of numbers whose product equals the original number. Follow the steps mentioned below to find the factors:

Step 1: Start to multiply with numbers, which gives the value of 72.

Start with 1, and continue to multiply by other numbers. 

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

Step 2: After the calculation, we get to these numbers, the factors of 72.

Step 3: The positive factor pairs of 72 are (1, 72), (2, 36), (3, 24), (4, 18), (6, 12), (8, 9)

Step 4: The negative factor pairs of 72 are (-1, -72), (-2, -36), (-3, -24), (-4, -18), (-6, -12), (-8, -9)
 

Using this method we will break down the given number until we get the remainder as zero. Let’s follow the steps mentioned below to find the factors of 72:

Step 1: Divide 72 by smaller numbers and see if there is any remainder. E.g., 72/1 = 72.

Step 2: Continue the process by checking other numbers as well. For 72, the factors are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72. Because 72 can be divided evenly by these numbers.
 

In the method of prime factorization, a number is broken down into the product of its prime factors. The prime factors can be found by following the steps below:

2 is the smallest prime number of 72, so start dividing by 2. Then continue to divide with other prime numbers.

72  ÷  2 = 36
36  ÷  2 = 18
18  ÷  2 = 9
9 ÷ 3 = 3

3÷3 = 1

 The prime factorization of 72 is: 72 = 2³ × 3²

With prime factorization, 72 can be broken down into prime factors, 2 and 3.
 

A factor tree is a graphical representation of breaking a composite number into its prime factors. It is an easy method to find out the factors of any number.

Step 1: 72 divided by 2 gives us the quotient 36. 

Step 2: Since 36 is not a prime number, it can be divided further.

72 ÷ 2 = 36
36  ÷ 2 = 18
18  ÷ 2 = 9
9 ÷3 = 3

 The prime factorization of 72 is written below : 
 72 =2³ × 3²
 

Every number has either a positive or negative factor. Let us look at those sets of factors.

Positive pair Factors:(1,72), (2,36), (3,24), (4,18), (6,12), and  (8,9).
Negative pair Factors: (-1,-72), (-2,-36), (-3,-24), (-4,-18), (-6,-12), and  (-8,-9).
 

• Factors: Factors are numbers that divide a given number exactly, without any remainder. For example, 6 is divisible by 1, 2, 3, and 6. Therefore, 1, 2, 3, and 6 are the factors of 6.

• Prime Factors: Prime factors of the numbers that multiply together to give a certain product. For 72, the prime factors are 2 and 3.

• Multiples: We get multiples when we multiply a number by another number. Let’s take some multiples of 2 (2, 4, 6, and so on).

• Composite Numbers: composite numbers are the numbers that have more than 2 factors. For example: The composite number of 10 is 1, 2, 5, and 10

• Negative Factors: These numbers are the negative counterparts of the positive factors of a number. For example: the negative factor of 10 is -1, -2, -5, -10.