What is the Greatest Common Factor of 31970 and 31984?

Greatest common factor (GCF) of 31970 and 31984 is 2.

GCF(31970,31984) = 2

We will now calculate the prime factors of 31970 and 31984, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31970 and 31984.

How to find the GCF of 31970 and 31984?

We will first find the prime factorization of 31970 and 31984. After we will calculate the factors of 31970 and 31984 and find the biggest common factor number .

Step-1: Prime Factorization of 31970

Prime factors of 31970 are 2, 5, 23, 139. Prime factorization of 31970 in exponential form is:

31970 = 2¹ × 5¹ × 23¹ × 139¹

Step-2: Prime Factorization of 31984

Prime factors of 31984 are 2, 1999. Prime factorization of 31984 in exponential form is:

31984 = 2⁴ × 1999¹

Step-3: Factors of 31970

List of positive integer factors of 31970 that divides 31970 without a remainder.

1, 2, 5, 10, 23, 46, 115, 139, 230, 278, 695, 1390, 3197, 6394, 15985

Step-4: Factors of 31984

List of positive integer factors of 31984 that divides 31970 without a remainder.

1, 2, 4, 8, 16, 1999, 3998, 7996, 15992

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31970 and 31984. The biggest common factor number is the GCF number.
So the greatest common factor 31970 and 31984 is 2.

Also check out the Least Common Multiple of 31970 and 31984