 # Factors of 100

The factors of 100 are the numbers, that produce the result as 100 when two numbers are multiplied together. Factor pairs of the number 100 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, 100, we will use the factorization method. In the factorization method, first take the numbers, 1 and 100 as factors of 100 and proceed with finding the other pair of multiples of 100 which gives the results as an original number. To understand this method in a better way, read the article below to find factor 100 in pairs and also the division method to find the prime factors of 100 is discussed.

## Pair Factors of 100

To find the positive and negative factor pairs of 100, multiply the two numbers in a pair to get the original number as 100, such numbers are as follows

 Positive Pair Factor Negative Pair Factor 1 × 100 = 100 ⇒ (1, 100) -1 × -100 = 100 ⇒ (-1, -100) 2 × 50 = 100 ⇒ (2, 50) -2 × -50 = 100 ⇒ (-2, -50) 4 × 25 = 100 ⇒ (4, 25) -4 × -25 = 100 ⇒ (-4, -25) 5 × 20 = 100 ⇒ (5, 20) -5 × -20 = 100 ⇒ (-5, -20) 10 × 10 = 100 ⇒ (10, 10) -10 × -10 = 100 ⇒ (-10, -10)

### How to calculate the Factors of 100?

Learn the following steps to calculate the factors of a number 100.

• First, write the number 100
• Find the two numbers, which gives the result as 100 under the multiplication, say 5 and 20, such as 5 × 20 = 100.
• We know that 5 is a prime number which has only two factors, i.e., 1 and the number itself (1 and 5) which cannot be further factorized.

5 = 5 × 1

• But look at the number 20, which is a composite number but not a prime number and it can be further factorized.

20 can be factorised as 2 x 2 x 5 x 5 x 1

• Therefore, the factorization of 100 is written as, 100 = 2 x 2 x 5 × 5 x 1
• Finally, write down all the unique numbers which we can obtain from 2 x 2 x 5 × 5 x 1
 Factors of 100 1, 2, 4, 5, 10, 20, 25, 50, and 100

### Prime Factors of 100 By Division Method

The number 100 is a composite and it should have prime factors. Now let us know how to calculate the prime factors of 100.

Step 1: The first step is to divide the number 100 with the smallest prime factor, say 2.

100 ÷ 2 = 50

Step 2: Again divide 32 by 2 and the process goes on.

50 ÷ 2 = 25

Step 3: You will get a fractional number if you divide 25 by 2. So continue with the next prime factor, say 5

25 ÷ 5 = 5

5 ÷ 5 = 1

Finally, we received the number 1 at the end of the division process. So that we cannot proceed further. So, the prime factors of 100 are written as 2 x 2 × 5 x 5 or 22 x 52, where 2 and 5 are the prime numbers.

It is possible to find the exact number of factors of a number 100 with the help of prime factorisation. The prime factor of the 100 is 22 x 52. The exponents in the prime factorisation are 2 and 2. Add the number 1 with the exponents and multiply it. (2+1)(2+1) = 3 x 3 = 9. Therefore, the number 100 has 9 factors.

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