What is the Greatest Common Factor of 84 and 100?

Greatest common factor (GCF) of 84 and 100 is 4.

GCF(84,100) = 4

We will now calculate the prime factors of 84 and 100, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 84 and 100.

How to find the GCF of 84 and 100?

We will first find the prime factorization of 84 and 100. After we will calculate the factors of 84 and 100 and find the biggest common factor number .

Step-1: Prime Factorization of 84

Prime factors of 84 are 2, 3, 7. Prime factorization of 84 in exponential form is:

84 = 2² × 3¹ × 7¹

Step-2: Prime Factorization of 100

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

100 = 2² × 5²

Step-3: Factors of 84

List of positive integer factors of 84 that divides 84 without a remainder.

1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42

Step-4: Factors of 100

List of positive integer factors of 100 that divides 84 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 84 and 100. The biggest common factor number is the GCF number.
So the greatest common factor 84 and 100 is 4.

Also check out the Least Common Multiple of 84 and 100