What is the Greatest Common Factor of 6 and 30?

Greatest common factor (GCF) of 6 and 30 is 6.

GCF(6,30) = 6

We will now calculate the prime factors of 6 and 30, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 6 and 30.

How to find the GCF of 6 and 30?

We will first find the prime factorization of 6 and 30. After we will calculate the factors of 6 and 30 and find the biggest common factor number .

Step-1: Prime Factorization of 6

Prime factors of 6 are 2, 3. Prime factorization of 6 in exponential form is:

6 = 2¹ × 3¹

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 6

List of positive integer factors of 6 that divides 6 without a remainder.

1, 2, 3

Step-4: Factors of 30

List of positive integer factors of 30 that divides 6 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 6 and 30. The biggest common factor number is the GCF number.
So the greatest common factor 6 and 30 is 6.

Also check out the Least Common Multiple of 6 and 30