Factors of 100

The numbers that divide 100 evenly are known as factors of 100. A factor of 100 is a number that divides the number without remainder. The factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, and 100.

Negative factors of 100: -1, -2, -4, -5, -10, -20, -25, -50, and -100.

Prime factors of 100: 2 and 5.

Prime factorization of 100: 2² × 5².

The sum of factors of 100: 1 + 2 + 4 + 5 + 10 + 20 + 25 + 50 + 100 = 217

Factors can be found using different methods. Mentioned below are some commonly used methods:

1. Finding factors using multiplication
2. Finding factors using division method
3. Prime factors and Prime factorization

To find factors using multiplication, we need to identify the pairs of numbers that are multiplied to give 100. Identifying the numbers which are multiplied to get the number 100 is the multiplication method.

Step 1: Multiply 100 by 1, 100 × 1 = 100.

Step 2: Check for other numbers that give 100 after multiplying 2 × 50 = 100

4 × 25 = 100

5 × 20 = 100

10 × 10 = 100

Therefore, the positive factor pairs of 100 are: (1, 100), (2, 50), (4, 25), (5, 20), and (10, 10). For every positive factor, there is a negative factor.

Dividing the given numbers with whole numbers until the remainder becomes zero and listing out the numbers which result as whole numbers as factors. Factors can be calculated by following a simple division method -

Step 1: Divide 100 by 1, 100 ÷ 1 = 100.

Step 2: Continue dividing 100 by the numbers until the remainder becomes 0.

100 ÷ 1 = 100

100 ÷ 2 = 50

100 ÷ 4 = 25

100 ÷ 5 = 20

100 ÷ 10 = 10

Therefore, the factors of 100 are: 1, 2, 4, 5, 10, 20, 25, 50, 100.

The factors can be found by dividing it with prime numbers. We can find the prime factors using the following methods:

• Using prime factorization
• Using factor tree

Using Prime Factorization: In this process, prime factors of 100 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.

100 ÷ 2 = 50

50 ÷ 2 = 25

25 ÷ 5 = 5

5 ÷ 5 = 1

The prime factors of 100 are 2 and 5. The prime factorization of 100 is: 2² × 5².

The factor tree is the graphical representation of breaking down any number into prime factors. The following steps show -

Step 1: Firstly, 100 is divided by 2 to get 50.

Step 2: Now divide 50 by 2 to get 25.

Step 3: Divide 25 by 5 to get 5. Here, 5 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 100 is: 2² × 5².

Factor Pairs : Two numbers that are multiplied to give a specific number are called factor pairs. Both positive and negative factors constitute factor pairs.

• Positive factor pairs of 100: (1, 100), (2, 50), (4, 25), (5, 20), and (10, 10).
• Negative factor pairs of 100: (-1, -100), (-2, -50), (-4, -25), (-5, -20), and (-10, -10).

• Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, and 100.

• Prime factors: The factors which are prime numbers. For example, 2 and 5 are prime factors of 100.

• Factor pairs: Two numbers in a pair that are multiplied to give the original number are called factor pairs. For example, the factor pairs of 100 are (1, 100), (2, 50), etc.

• Prime factorization: The expression of a number as a product of its prime factors. For example, the prime factorization of 100 is 2² × 5².

• Multiples: A multiple of a number is the product of that number and an integer. For example, 100 is a multiple of 4 because 4 × 25 = 100.