What is the Greatest Common Factor of 74675 and 74688?

Greatest common factor (GCF) of 74675 and 74688 is 1.

GCF(74675,74688) = 1

We will now calculate the prime factors of 74675 and 74688, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 74675 and 74688.

How to find the GCF of 74675 and 74688?

We will first find the prime factorization of 74675 and 74688. After we will calculate the factors of 74675 and 74688 and find the biggest common factor number .

Step-1: Prime Factorization of 74675

Prime factors of 74675 are 5, 29, 103. Prime factorization of 74675 in exponential form is:

74675 = 5² × 29¹ × 103¹

Step-2: Prime Factorization of 74688

Prime factors of 74688 are 2, 3, 389. Prime factorization of 74688 in exponential form is:

74688 = 2⁶ × 3¹ × 389¹

Step-3: Factors of 74675

List of positive integer factors of 74675 that divides 74675 without a remainder.

1, 5, 25, 29, 103, 145, 515, 725, 2575, 2987, 14935

Step-4: Factors of 74688

List of positive integer factors of 74688 that divides 74675 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 192, 389, 778, 1167, 1556, 2334, 3112, 4668, 6224, 9336, 12448, 18672, 24896, 37344

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 74675 and 74688. The biggest common factor number is the GCF number.
So the greatest common factor 74675 and 74688 is 1.

Also check out the Least Common Multiple of 74675 and 74688