What is the Greatest Common Factor of 100 and 105?

Greatest common factor (GCF) of 100 and 105 is 5.

GCF(100,105) = 5

We will now calculate the prime factors of 100 and 105, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 100 and 105.

How to find the GCF of 100 and 105?

We will first find the prime factorization of 100 and 105. After we will calculate the factors of 100 and 105 and find the biggest common factor number .

Step-1: Prime Factorization of 100

Prime factors of 100 are 2, 5. Prime factorization of 100 in exponential form is:

100 = 2² × 5²

Step-2: Prime Factorization of 105

Prime factors of 105 are 3, 5, 7. Prime factorization of 105 in exponential form is:

105 = 3¹ × 5¹ × 7¹

Step-3: Factors of 100

List of positive integer factors of 100 that divides 100 without a remainder.

1, 2, 4, 5, 10, 20, 25, 50

Step-4: Factors of 105

List of positive integer factors of 105 that divides 100 without a remainder.

1, 3, 5, 7, 15, 21, 35

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 100 and 105. The biggest common factor number is the GCF number.
So the greatest common factor 100 and 105 is 5.

Also check out the Least Common Multiple of 100 and 105