What is the Greatest Common Factor of 3100 and 3120?

Greatest common factor (GCF) of 3100 and 3120 is 20.

GCF(3100,3120) = 20

We will now calculate the prime factors of 3100 and 3120, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 3100 and 3120.

How to find the GCF of 3100 and 3120?

We will first find the prime factorization of 3100 and 3120. After we will calculate the factors of 3100 and 3120 and find the biggest common factor number .

Step-1: Prime Factorization of 3100

Prime factors of 3100 are 2, 5, 31. Prime factorization of 3100 in exponential form is:

3100 = 2² × 5² × 31¹

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 3100

List of positive integer factors of 3100 that divides 3100 without a remainder.

1, 2, 4, 5, 10, 20, 25, 31, 50, 62, 100, 124, 155, 310, 620, 775, 1550

Step-4: Factors of 3120

List of positive integer factors of 3120 that divides 3100 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 3100 and 3120. The biggest common factor number is the GCF number.
So the greatest common factor 3100 and 3120 is 20.

Also check out the Least Common Multiple of 3100 and 3120