Factors of 144 – Prime Factorization | Easy Method

Factors of 144

The factors of 144 are the numbers, which produce the result of 144 when two numbers are multiplied together.

Factor pairs of 144 can be either positive or negative and are not fractions or decimals. Using the factorization method, we can find the factors of the number 144. For a better understanding of the factorization method, read this article that discusses finding 144 in pairs and also how to find its prime factors.

As an example, the factor pair for 73 can be written as (1, 73) and (-1, 73). When we multiply two negative factors, the result should be the original number, for example multiplying -1 * -73 gives us 73. Therefore, we can consider both positive and negative pairs of 73.

What are the Factors of 144?

The factors of 144 are the numbers that divide the number 144 exactly without leaving any remainders. Factors of 144 are the pairs of numbers multiplied together, resulting in 144. The number 144 has more than two factors since it is a composite number. There are 15 factors in the number 144.

What are the Factors of -144?

When we multiply two numbers, and we get -144 as a product, those numbers are the factors of -144. 

Here is the explanation:

-1 × 144 = -144

 1 × -144 = -144

 -2 × 72 = -144

 2 × -72 = -144

 -3 × 48 = -144

 3 × -48 = -144

 -4 × 36 = -144

 4 × -36 = -144

 -6 × 24 = -144

 6 × -24 = -144

 -8 × 18 = -144

 8 × -18 = -144

 -9 × 16 = -144

 9 × -16 = -144

 -12 × 12 = -144

 12 × -12 = -144

We can get -144 by having (-1, 144), (-2, 72), (-3, 48), (-4, 36), (-6, 24), (-8, 18), (-9, 16), and (-12, 12) as a pair of factors. Similarly, we can also get -144 by having  (1, -144), (2, -72), (3, -48), (4, -36), (6, -24), (8, -18), (9, -16), and (12, -12)as a pair of factors.

Pair Factors of 144

The pair factors can be found by multiplying the two numbers in a pair to get 144, as follows:

How to calculate the Prime Factors of 144?

Follow these steps to calculate the factors of 144.

• Start by writing the number 144
• Find the two numbers that multiply to 144 under the multiplication, such as 2 and 72, 

such as 2 × 72 = 144.

• It is known that 2 has only two factors, namely 1 and the number itself (which cannot be further factorized). 2 = 2 × 1

• Look at the number 72, which is not a prime number, but is a composite number, and can be further factorized. 72 can be factorized as 2 × 2 × 2 × 3 × 3 × 1
• So, the factorization of 144 is 144 = 2 × 2 × 2 × 2 × 3 × 3 × 1
• As a final step, write down all the unique numbers that you obtained as factors.

Prime Factorization of 144

As a composite number, 144 should have prime factors. Let’s see how prime factors are determined.

Step 1:

The first step is to divide the number 144 by the smallest prime factor, which is 2.

144 ÷ 2 = 72

Step 2:

Divide 72 by 2 again and repeat the process.

72 ÷ 2 = 36

36 ÷ 2 = 18

18 ÷ 2 = 9

Step 3:

If you divide 9 by 2, you will obtain a fractional number.  So, continue with the next prime factor, 3

9 ÷ 3 = 3

3 ÷ 3 = 1

As a result of the division process, we received number 1. Therefore, we cannot proceed. Thus, the prime factors are written as 2 × 2 × 2 × 2 * 2 × 3 × 3 or 24 × 32, where 2 and 3 are prime numbers.

By using prime factorization, you can determine how many factors 144 contains. 144 has 24 × 32 prime factors. The exponents of the prime factorization are 4 and 2. Then multiply 1 by these exponents. (4+1)(2+1) = 5 × 3 = 15. Thus, 144 has 15 factors.

Solved Examples

Example 1:

Calculate the common factors of 144 and 150.

Solution:

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

Factors of 50 = 1, 2, 4, 5, 10, 20, 25, 50, and 100.

Thus, the common factor of 144 and 150 is 1, 2, and 4.

Example 2:

Calculate the common factors of 46 and 24.

Solution:

Factors of 46 = 1, 2, 23, and 46.

Factors of 24= 1, 2, 3, 4, 6, 8, 12, and 24.

Thus, the common factor of 46 and 24 are 1 and 2.

Example 3:

Find out the common factors of 144 and 35.

Solution:

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

All 35 factors=  1, 5, 7, and 35.

Therefore, the common factor of 144 and 35 is 1.

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