What is the Greatest Common Factor of 3120 and 3138?

Greatest common factor (GCF) of 3120 and 3138 is 6.

GCF(3120,3138) = 6

We will now calculate the prime factors of 3120 and 3138, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 3120 and 3138.

How to find the GCF of 3120 and 3138?

We will first find the prime factorization of 3120 and 3138. After we will calculate the factors of 3120 and 3138 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 3138

Prime factors of 3138 are 2, 3, 523. Prime factorization of 3138 in exponential form is:

3138 = 2¹ × 3¹ × 523¹

Step-3: Factors of 3120

List of positive integer factors of 3120 that divides 3120 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

Step-4: Factors of 3138

List of positive integer factors of 3138 that divides 3120 without a remainder.

1, 2, 3, 6, 523, 1046, 1569

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 3120 and 3138. The biggest common factor number is the GCF number.
So the greatest common factor 3120 and 3138 is 6.

Also check out the Least Common Multiple of 3120 and 3138