The factors of 144 are the numbers, that produce the result as 144 when two numbers are multiplied together. Factor pairs of the number 144 are the whole numbers which could be either positive or negative but not a fraction or decimal number. To find the factors of a number, 144, we will use the factorization method. To understand the factorisation method in a better way, read the below article to find factor 144 in pairs and also the division method to find the prime factors of 144 is discussed.

Consider an example, the factor pair of 73 is written as (1, 73) and (-1,-73). When we multiply the pair of negative factors, the result should give the original number, such as multiplying -1  × -73, then we get the number 73. Thus, we can consider both positive and negative factor pairs of 73.

Table of Contents:

• • What are the Factors of 144?
  • Pair Factors of 144
  • How to Find the Prime Factors of 144?
  • Prime Factorization of 144
  • Examples
  • FAQs

What are the Factors of 144?

The factors of 144 are the numbers that divide the number 144 exactly without leaving the remainder. In other words, the factors of 144 are the numbers that are multiplied in pairs resulting in the number 144. As the number 144 is a composite number, it has more than two factors. The number 144 has 15 factors.

Pair Factors of 144

To find the pair factors, multiply the two numbers in a pair to get the original number as 144, such numbers are as follows

How to calculate the Prime Factors of 144?

Learn the following steps to calculate the factors of a number 144.

• • First, write the number 144
  • Find the two numbers, which gives the result as 144 under the multiplication, say 2 and 72, such as 2 × 72 = 144.
  • We know that 2 is a prime number that has only two factors, i.e., 1 and the number itself (1 and 2) which cannot be further factorized. 2 = 2 × 1

• • But look at the number 72, which is a composite number but not a prime number and it can be further factorized. 72 can be factorised as 2 x 2 x 2 x 3 x 3 x 1
  • Therefore, the factorization of 144 is written as, 144 = 2 x 2 x 2 x 2 x 3 x 3 x 1
  • Finally, write down all the unique numbers that are obtained as factors.

Prime Factorization of 144

The number 144 is a composite and it should have prime factors. Now let us know how to calculate the prime factors of a number

Step 1: The first step is to divide the number 144 with the smallest prime factor, say 2.

144 ÷ 2 = 72

Step 2: Again divide 72 by 2 and the process goes on.

72 ÷ 2 = 36

36 ÷ 2 = 18

18 ÷ 2 = 9

Step 3: You will get a fractional number if you divide 9 by 2. So, continue with the next prime factor, say 3

9 ÷ 3 = 3

3 ÷ 3 = 1

Finally, we received the number 1 at the end of the division process. So that we cannot proceed further. So, the prime factors are written as  2 x 2 x 2 x 2 × 3 x 3 or 2⁴ x 3², where 2 and 3 are the prime numbers.

It is possible to find the exact number of factors of a number 144 with the help of prime factorisation. The prime factor of the 144 is 2⁴ x 3². The exponents in the prime factorisation are 4 and 2. Add the number 1 with the exponents and multiply it. (4+1)(2+1) = 5 x 3 = 15. Therefore, the number 144 has 15 factors.

Examples

Example 1:

Find the common factors of 144 and 143

Solution:

The factors of 144 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, and 144

The factors of 143 are 1, 11, 13 and 143

Therefore, the common factor of 144 and 143 is 1.

Example 2:

Find the common factors of 144 and 145

Solution:

Factors of 144 = 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, and 144

Factors of 145 = 1, 5, 29, and 145

Therefore, the common factor of 144 and 145 is 1.

Example 3:

Find the common factors of 144 and 141.

Solution:

The factors of 144 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, and 144

The factors of 141 are 1, 3, 47, and 141.

Thus, the common factors of 144 and 141 are 1 and 3.

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