Factors of 100 | with Easy division and prime factorization

Factors of 100

The factors of 100 are the numbers that are multiplied together to produce the result of 100.

In the factor pair 100, no fraction or decimal numbers are allowed. Both the whole number and the fraction pair must be positive or negative. We will use the factorization method to find the factors of a number, 100. 

Using the factorization method, find the other multiples of 100 which gives the original number by first taking 1 and 100 as factors of 100. By using the prime factorization and many solved examples, you will learn the factors of 100, the pair factors of 100, and the prime factors of 100.

What are the Factors of 100?

A factor of 100 is any number that divides 100 exactly without leaving any remainder. In other words, the factors of 100 are the pairs of numbers that result in the original number 100. Since 100 is an even composite number, the number 100 has many factors besides 1 and the number itself. Therefore, the factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, and 100.

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

Prime Factorization of 100: 2 × 2 × 5 × 5 or 22 × 52.

What are the Factors of -100?

When we multiply two numbers, and we get -100 as a product, those numbers are the factors of -100. Here is the explanation:

 -1 × 100 = -100

  1 × -100 = -100

-2 × 50 = -100  

  2 × -50 = -100 

 -4 × 25 = -100 

  4 × -25 = -100 

-5 × 20 = -100 

5 × -20 = -100 

-10× 10 = -100 

10  × -10 = -100

We can get -100 by having (-1, 100), (-2, 50), (-4, 25), (-5, 20), and (-10, 10) as a pair of factors. Similarly, we can also get -100 by having (1, -100), (2, -50), (4, -25), (5, -20), and(10,-10) as a pair of factors.

Pair Factors of 100

In order to find the positive and negative factors of 100, multiply the two numbers in a pair to get the original number, for example:

Therefore, the positive pair factors of 100 are (1, 100), (2, 50), (4, 25), (5, 20), and (10, 10). Similar to the positive pair factors, the negative pair factors of 100 are (-1, -100), (-2, -50), (-4, -25), (-5, -20), and (-10, -10). 

Factors of 100 by Division Method

Using the division method, one can find the factors of 100. In the division method, 100 is divided by consecutive integers. Those integers are factors of 100 if they divide 100 exactly. First, start dividing 100 by 1 and continue with the consecutive integers.

• 100/1 = 100     (Factor is 1 and Remainder is 0)
• 100/2 = 50       (Factor is 2 and Remainder is 0)
• 100/4 = 25       (Factor is 4 and Remainder is 0)
• 100/5 = 20       (Factor is 5 and Remainder is 0)
• 100/10 = 10     (Factor is 10 and Remainder is 0)
• 100/20 = 5       (Factor is 20 and Remainder is 0)
• 100/25 = 4       (Factor is 25  and Remainder is 0)
• 100/50 = 2       (Factor is 50 and Remainder is 0)
• 100/100 = 1    (Factor is 100 and Remainder is 0)

Therefore, there are 1, 2, 4, 5, 10, 20, 25, 50, and 100 factors of 100. When we divide 100 by different numbers other than 1, 2, 4, 5, 10, 20, 25, 50, and 100, there is a remainder and thus these are not factors of 100.

Prime Factorization of 100

As a composite number, 100 should have prime factors. Let’s find out how to find 100’s prime factors.

Step 1: 

The first step is to divide 100 by the smallest prime factor, say 2.

100 ÷ 2 = 50

Step 2:

Divide 50 by 2 again and repeat the process.

50 ÷ 2 = 25

Step 3:

If you divide 25 by 2 and 3, you will get a fraction. Now let’s look at the next prime number, say 5.

25 ÷ 5 = 5

5 ÷ 5 = 1

In the end, we received number 1 at the end of the division process. Therefore, we cannot move forward. Therefore, the prime factors of 100 are 2 x 2 * 5 x 5 or 22 x 52, where 2 and 5 are prime numbers.

The prime factorization method makes it possible to find the exact number of factors of the number 100. 100 has a prime factor of 22 x 52. There are two exponents in the prime factorization. Multiply the number 1 with the exponents. (2+1)(2+1) = 3 x 3 = 9. As a result, the number 100 has nine factors.

Solved Examples

Example 1:

Calculate the common factors of 100 and 19.

Solution:

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

Factors of 19 =  1 and 19.

Since 101 is a prime number, the common factor for 100 and 19 is 1.

Example 2:

Find the common factors of 53 and 47.

Solution:

Factors of 53 = 1 and 53.

Pairs of 47 = 1 and 47.

100 and 47 have only one thing in common: 1.

Example 3:

Calculate the common factor of 100 and 24.

Solution:

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

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

Therefore, the common factors of 100 and 50 are 1, 2, and 4.

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