What is the Greatest Common Factor of 17969 and 17976?

Greatest common factor (GCF) of 17969 and 17976 is 7.

GCF(17969,17976) = 7

We will now calculate the prime factors of 17969 and 17976, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17969 and 17976.

How to find the GCF of 17969 and 17976?

We will first find the prime factorization of 17969 and 17976. After we will calculate the factors of 17969 and 17976 and find the biggest common factor number .

Step-1: Prime Factorization of 17969

Prime factors of 17969 are 7, 17, 151. Prime factorization of 17969 in exponential form is:

17969 = 7¹ × 17¹ × 151¹

Step-2: 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-3: Factors of 17969

List of positive integer factors of 17969 that divides 17969 without a remainder.

1, 7, 17, 119, 151, 1057, 2567

Step-4: Factors of 17976

List of positive integer factors of 17976 that divides 17969 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17969 and 17976. The biggest common factor number is the GCF number.
So the greatest common factor 17969 and 17976 is 7.

Also check out the Least Common Multiple of 17969 and 17976