What is the Greatest Common Factor of 31970 and 31978?

Greatest common factor (GCF) of 31970 and 31978 is 2.

GCF(31970,31978) = 2

We will now calculate the prime factors of 31970 and 31978, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31970 and 31978.

How to find the GCF of 31970 and 31978?

We will first find the prime factorization of 31970 and 31978. After we will calculate the factors of 31970 and 31978 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 31978

Prime factors of 31978 are 2, 59, 271. Prime factorization of 31978 in exponential form is:

31978 = 2¹ × 59¹ × 271¹

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 31978

List of positive integer factors of 31978 that divides 31970 without a remainder.

1, 2, 59, 118, 271, 542, 15989

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31970 and 31978. The biggest common factor number is the GCF number.
So the greatest common factor 31970 and 31978 is 2.

Also check out the Least Common Multiple of 31970 and 31978