What is the Greatest Common Factor of 30 and 312?

Greatest common factor (GCF) of 30 and 312 is 6.

GCF(30,312) = 6

We will now calculate the prime factors of 30 and 312, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30 and 312.

How to find the GCF of 30 and 312?

We will first find the prime factorization of 30 and 312. After we will calculate the factors of 30 and 312 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 312

Prime factors of 312 are 2, 3, 13. Prime factorization of 312 in exponential form is:

312 = 2³ × 3¹ × 13¹

Step-3: Factors of 30

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

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

Step-4: Factors of 312

List of positive integer factors of 312 that divides 30 without a remainder.

1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30 and 312. The biggest common factor number is the GCF number.
So the greatest common factor 30 and 312 is 6.

Also check out the Least Common Multiple of 30 and 312