What is the Greatest Common Factor of 17976 and 17985?

Greatest common factor (GCF) of 17976 and 17985 is 3.

GCF(17976,17985) = 3

We will now calculate the prime factors of 17976 and 17985, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17976 and 17985.

How to find the GCF of 17976 and 17985?

We will first find the prime factorization of 17976 and 17985. After we will calculate the factors of 17976 and 17985 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 17985

Prime factors of 17985 are 3, 5, 11, 109. Prime factorization of 17985 in exponential form is:

17985 = 3¹ × 5¹ × 11¹ × 109¹

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 17985

List of positive integer factors of 17985 that divides 17976 without a remainder.

1, 3, 5, 11, 15, 33, 55, 109, 165, 327, 545, 1199, 1635, 3597, 5995

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17976 and 17985. The biggest common factor number is the GCF number.
So the greatest common factor 17976 and 17985 is 3.

Also check out the Least Common Multiple of 17976 and 17985