What is the Greatest Common Factor of 8 and 21?

Greatest common factor (GCF) of 8 and 21 is 1.

GCF(8,21) = 1

We will now calculate the prime factors of 8 and 21, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 8 and 21.

How to find the GCF of 8 and 21?

We will first find the prime factorization of 8 and 21. After we will calculate the factors of 8 and 21 and find the biggest common factor number .

Step-1: Prime Factorization of 8

Prime factors of 8 are 2. Prime factorization of 8 in exponential form is:

8 = 2³

Step-2: Prime Factorization of 21

Prime factors of 21 are 3, 7. Prime factorization of 21 in exponential form is:

21 = 3¹ × 7¹

Step-3: Factors of 8

List of positive integer factors of 8 that divides 8 without a remainder.

1, 2, 4

Step-4: Factors of 21

List of positive integer factors of 21 that divides 8 without a remainder.

1, 3, 7

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 8 and 21. The biggest common factor number is the GCF number.
So the greatest common factor 8 and 21 is 1.

Also check out the Least Common Multiple of 8 and 21