What is the Greatest Common Factor of 3114 and 3120?

Greatest common factor (GCF) of 3114 and 3120 is 6.

GCF(3114,3120) = 6

We will now calculate the prime factors of 3114 and 3120, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 3114 and 3120.

How to find the GCF of 3114 and 3120?

We will first find the prime factorization of 3114 and 3120. After we will calculate the factors of 3114 and 3120 and find the biggest common factor number .

Step-1: Prime Factorization of 3114

Prime factors of 3114 are 2, 3, 173. Prime factorization of 3114 in exponential form is:

3114 = 2¹ × 3² × 173¹

Step-2: Prime Factorization of 3120

Prime factors of 3120 are 2, 3, 5, 13. Prime factorization of 3120 in exponential form is:

3120 = 2⁴ × 3¹ × 5¹ × 13¹

Step-3: Factors of 3114

List of positive integer factors of 3114 that divides 3114 without a remainder.

1, 2, 3, 6, 9, 18, 173, 346, 519, 1038, 1557

Step-4: Factors of 3120

List of positive integer factors of 3120 that divides 3114 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 13, 15, 16, 20, 24, 26, 30, 39, 40, 48, 52, 60, 65, 78, 80, 104, 120, 130, 156, 195, 208, 240, 260, 312, 390, 520, 624, 780, 1040, 1560

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 3114 and 3120. The biggest common factor number is the GCF number.
So the greatest common factor 3114 and 3120 is 6.

Also check out the Least Common Multiple of 3114 and 3120