What is the Greatest Common Factor of 6975 and 6980?

Greatest common factor (GCF) of 6975 and 6980 is 5.

GCF(6975,6980) = 5

We will now calculate the prime factors of 6975 and 6980, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 6975 and 6980.

How to find the GCF of 6975 and 6980?

We will first find the prime factorization of 6975 and 6980. After we will calculate the factors of 6975 and 6980 and find the biggest common factor number .

Step-1: Prime Factorization of 6975

Prime factors of 6975 are 3, 5, 31. Prime factorization of 6975 in exponential form is:

6975 = 3² × 5² × 31¹

Step-2: Prime Factorization of 6980

Prime factors of 6980 are 2, 5, 349. Prime factorization of 6980 in exponential form is:

6980 = 2² × 5¹ × 349¹

Step-3: Factors of 6975

List of positive integer factors of 6975 that divides 6975 without a remainder.

1, 3, 5, 9, 15, 25, 31, 45, 75, 93, 155, 225, 279, 465, 775, 1395, 2325

Step-4: Factors of 6980

List of positive integer factors of 6980 that divides 6975 without a remainder.

1, 2, 4, 5, 10, 20, 349, 698, 1396, 1745, 3490

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 6975 and 6980. The biggest common factor number is the GCF number.
So the greatest common factor 6975 and 6980 is 5.

Also check out the Least Common Multiple of 6975 and 6980