What is the Greatest Common Factor of 31970 and 31990?

Greatest common factor (GCF) of 31970 and 31990 is 10.

GCF(31970,31990) = 10

We will now calculate the prime factors of 31970 and 31990, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31970 and 31990.

How to find the GCF of 31970 and 31990?

We will first find the prime factorization of 31970 and 31990. After we will calculate the factors of 31970 and 31990 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 31990

Prime factors of 31990 are 2, 5, 7, 457. Prime factorization of 31990 in exponential form is:

31990 = 2¹ × 5¹ × 7¹ × 457¹

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 31990

List of positive integer factors of 31990 that divides 31970 without a remainder.

1, 2, 5, 7, 10, 14, 35, 70, 457, 914, 2285, 3199, 4570, 6398, 15995

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31970 and 31990. The biggest common factor number is the GCF number.
So the greatest common factor 31970 and 31990 is 10.

Also check out the Least Common Multiple of 31970 and 31990