[Maths Class Notes] on Factors of 144 Pdf for Exam

Factor, in arithmetic, is a number or algebraic expression that divides every quantity or expression (of which it is a factor) uniformly, which means without any remainder. For example, 4 and 2 are factors of 8, when multiplied together, the result is 8. 

Similarly, factors of 144 would be all the pairs of numbers, which, when multiplied together, give the result as 144. Now the question that arises is what the factors of 144 and how to find them are?

To start with, the factors of 144 are 1, 4, 2, 3, 6, 8, 16, 9, 12, 18, 24, 36, 48, 72 and 144. Now that the ‘what are the factors of 144’ is solved, the next step would be to figure out how to find these factors, and there are various methods to figure out a number’s factors, such as:

Prime Factorization of 144

Prime Factorization of 144 by division method is the first way to calculate a number’s factors.

We’ll start by dividing the number, i.e., 144 by the smallest integer, which is 2.

The process will start with, 144 ÷ 2 = 72

Then, 72 ÷ 2 = 36

36 ÷ 2 = 18

18 ÷ 2 = 9

Now that two can’t be divided with nine further without getting a decimal number, we’ll move onto the next integer, that is, 3.

Now, 9 ÷ 3 = 3

And, 3 ÷ 3 = 1

Prime Factorization Explained Through Diagrammatic Means

144 =

2 |144

2 |72

2 |36

2 |18

3 |9

3 |3

     1 

144 = 2 x 2 x 2 x 2 x 3 x 3

When the final outcome is 1 that is when we stop the division process as we can’t go further than this. So, the prime factors of 144 are written in a format of 2 x 2 x 2 x 2 × 3 x 3 or 24 x 32, where 2 and 3 are the prime numbers.

Similarly, we can group two numbers which when multiplied together gives us the result as 144, which is also called Pair Factors.

Pair Factors Method

What are the Factors of 144?

When calculated and counted, we concluded that the number 144 has 15 positive as well as 15 negative factors. Thus, there are 30 factors of 144 in total.

Exponential Form of 144

The exponential form is a compact way of representing a number. For example, instead of writing 2 × 2 × 2 × 2 = 16, we can always express it as 24.

Similarly, the prime factorization of 144 using exponents would be, 2 × 2 × 2 × 2 × 3 × 3 = 24 × 32.

Fun Facts

• 144 is a composite number as well as a perfect square. 144 could also be called a dozen dozens as well as it is 1 x 12. Another fact is that 144 is a perfect square as the square root of the number 144 is 12. Thus, the square root of 144 is an integer and 144 is a perfect square.

• 144 is a perfect square, yes, but the sum of its digits is also a perfect square, i.e., 9 (1 + 4 + 4 ), the product of its digits is also a perfect square, i.e.16, and its reverse is also a perfect square, i.e., 441.

From our context, we got to learn the following things on the factors of 144:

Factor Pairs: 144 = 1 x 144, 3 x 48, 2 x 72, 4 x 36, 8 x 18, 6 x 24, 9 x 16, 12 x 12.

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

Prime Factorization: 144 = 2 x 2 x 2 x 2 x 3 x 3. 

Prime Factorization of 144 using Exponents: 2 x 2 x 2 x 2 × 3 x 3 =  24 × 32