What is the Greatest Common Factor of 15974 and 15982?

Greatest common factor (GCF) of 15974 and 15982 is 2.

GCF(15974,15982) = 2

We will now calculate the prime factors of 15974 and 15982, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 15974 and 15982.

How to find the GCF of 15974 and 15982?

We will first find the prime factorization of 15974 and 15982. After we will calculate the factors of 15974 and 15982 and find the biggest common factor number .

Step-1: Prime Factorization of 15974

Prime factors of 15974 are 2, 7, 163. Prime factorization of 15974 in exponential form is:

15974 = 2¹ × 7² × 163¹

Step-2: Prime Factorization of 15982

Prime factors of 15982 are 2, 61, 131. Prime factorization of 15982 in exponential form is:

15982 = 2¹ × 61¹ × 131¹

Step-3: Factors of 15974

List of positive integer factors of 15974 that divides 15974 without a remainder.

1, 2, 7, 14, 49, 98, 163, 326, 1141, 2282, 7987

Step-4: Factors of 15982

List of positive integer factors of 15982 that divides 15974 without a remainder.

1, 2, 61, 122, 131, 262, 7991

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 15974 and 15982. The biggest common factor number is the GCF number.
So the greatest common factor 15974 and 15982 is 2.

Also check out the Least Common Multiple of 15974 and 15982