What is the Greatest Common Factor of 21 and 30?

Greatest common factor (GCF) of 21 and 30 is 3.

GCF(21,30) = 3

We will now calculate the prime factors of 21 and 30, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21 and 30.

How to find the GCF of 21 and 30?

We will first find the prime factorization of 21 and 30. After we will calculate the factors of 21 and 30 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 30

Prime factors of 30 are 2, 3, 5. Prime factorization of 30 in exponential form is:

30 = 2¹ × 3¹ × 5¹

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 30

List of positive integer factors of 30 that divides 21 without a remainder.

1, 2, 3, 5, 6, 10, 15

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21 and 30. The biggest common factor number is the GCF number.
So the greatest common factor 21 and 30 is 3.

Also check out the Least Common Multiple of 21 and 30