What is the Greatest Common Factor of 31972 and 31976?

Greatest common factor (GCF) of 31972 and 31976 is 4.

GCF(31972,31976) = 4

We will now calculate the prime factors of 31972 and 31976, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31972 and 31976.

How to find the GCF of 31972 and 31976?

We will first find the prime factorization of 31972 and 31976. After we will calculate the factors of 31972 and 31976 and find the biggest common factor number .

Step-1: Prime Factorization of 31972

Prime factors of 31972 are 2, 7993. Prime factorization of 31972 in exponential form is:

31972 = 2² × 7993¹

Step-2: Prime Factorization of 31976

Prime factors of 31976 are 2, 7, 571. Prime factorization of 31976 in exponential form is:

31976 = 2³ × 7¹ × 571¹

Step-3: Factors of 31972

List of positive integer factors of 31972 that divides 31972 without a remainder.

1, 2, 4, 7993, 15986

Step-4: Factors of 31976

List of positive integer factors of 31976 that divides 31972 without a remainder.

1, 2, 4, 7, 8, 14, 28, 56, 571, 1142, 2284, 3997, 4568, 7994, 15988

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31972 and 31976. The biggest common factor number is the GCF number.
So the greatest common factor 31972 and 31976 is 4.

Also check out the Least Common Multiple of 31972 and 31976