Factors of 100

The factors of 100 are defined as the numbers which when divided to 100 should not leave any remainder. This means, 100 must be completely divisible by such a number that it does not leave any remainder.

• The factors of a number are finite. It means, universally, that number will have a particular number of factors only.
• Composite numbers can only be factored in because they are made from the product of two or more numbers.
• Only integers and whole numbers can be factored in and will have factors.
• Every factor of a number is equal to less than the number itself.

The integer 100 can be divided only into two numbers – 1, 2, and 50. It means, the product of 2 and 50 will result in the number 100.
Moreover, the number 100 will have the following factors: 1, 2, 2, 5, and 5.
Therefore, the largest factor of 100 is 50, which is a composite number. The largest prime factor of 100 is 5. The number 100 can be written as: 100 = 2 x 2 x 5 x 5.

However, 100 will have the following categories of factors-
Positive factors: 1, 2, 4, 5, 10, 20, 25, 50 and 100.
Prime factors: 1, 2, 5
Negative factors: -2, -4, -5, -10, -20, -25, -50 and -100.
Prime factorization of 100 = 2 x 2 x 5 x 5

How to find the factors of 100?

The factors of 100 can be found by two methods –Long-division method and Prime factorization method.

Prime factorization method to find factors of 100

The prime factorization method is the most common method to represent several numbers, including 100. Prime factorization also has another form, the prime factor tree method, which is a visual method to represent factors of 100. It helps in determining various prime factors of 100. A factor tree is not unique for a given number. Instead of expressing 100 as 50 x 2, 25 x 4, or 5 x 20, we can represent 100 as 2 x 2 x 5 x 5.
We need to divide 100, from the smallest number to the largest number so that it completely divides the number-

• With the help of divisibility rules, we need to find out the smallest factor of the given number. Here, we have 100, which is an even number. Every even number is divisible by 2. In other words, 2 is the smallest prime factor of every even number. 100 ÷ 2 = 50. 2 divides 100 completely leaving no remainder.
• We can see the last digit of 100 is 0. When the last digit of any number ends with 0 or 5, it means the number is divisible by 5. Therefore, 100 ÷ 5 = 20. This means 5 is another prime factor of 100.
• Furthermore, 50 and 20 can be divided as: 50 = 5 x 10, and 20 = 2 x 10. It means 10 is another factor of 100.
• We need to find the factors till we get the remainder 0 in the end.
• 10 ÷ 2 = 5, and 5 ÷ 5 = 1. Here, we get remainder = 0. After this, our process is completed, and we get factors of 100.

Prime factorization of 100 using the prime factorization method is 2 x 2 x 5 x 5.

Example 1: What are the common factors of 100 and 101?

Solution: The factors of 100 = 2 x 2 x 5 x 5 The factors of 101 are 1, 101 (as 101 is a prime number). Thus, the common factors of 100 and 101 are 1 only.