What is the Greatest Common Factor of 17976 and 17983?

Greatest common factor (GCF) of 17976 and 17983 is 7.

GCF(17976,17983) = 7

We will now calculate the prime factors of 17976 and 17983, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17976 and 17983.

How to find the GCF of 17976 and 17983?

We will first find the prime factorization of 17976 and 17983. After we will calculate the factors of 17976 and 17983 and find the biggest common factor number .

Step-1: Prime Factorization of 17976

Prime factors of 17976 are 2, 3, 7, 107. Prime factorization of 17976 in exponential form is:

17976 = 2³ × 3¹ × 7¹ × 107¹

Step-2: Prime Factorization of 17983

Prime factors of 17983 are 7, 367. Prime factorization of 17983 in exponential form is:

17983 = 7² × 367¹

Step-3: Factors of 17976

List of positive integer factors of 17976 that divides 17976 without a remainder.

1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, 107, 168, 214, 321, 428, 642, 749, 856, 1284, 1498, 2247, 2568, 2996, 4494, 5992, 8988

Step-4: Factors of 17983

List of positive integer factors of 17983 that divides 17976 without a remainder.

1, 7, 49, 367, 2569

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17976 and 17983. The biggest common factor number is the GCF number.
So the greatest common factor 17976 and 17983 is 7.

Also check out the Least Common Multiple of 17976 and 17983