What is the Greatest Common Factor of 21 and 70?

Greatest common factor (GCF) of 21 and 70 is 7.

GCF(21,70) = 7

We will now calculate the prime factors of 21 and 70, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21 and 70.

How to find the GCF of 21 and 70?

We will first find the prime factorization of 21 and 70. After we will calculate the factors of 21 and 70 and find the biggest common factor number .

Step-1: Prime Factorization of 21

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

21 = 3¹ × 7¹

Step-2: Prime Factorization of 70

Prime factors of 70 are 2, 5, 7. Prime factorization of 70 in exponential form is:

70 = 2¹ × 5¹ × 7¹

Step-3: Factors of 21

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

1, 3, 7

Step-4: Factors of 70

List of positive integer factors of 70 that divides 21 without a remainder.

1, 2, 5, 7, 10, 14, 35

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21 and 70. The biggest common factor number is the GCF number.
So the greatest common factor 21 and 70 is 7.

Also check out the Least Common Multiple of 21 and 70