What is the Greatest Common Factor of 74688 and 74708?

Greatest common factor (GCF) of 74688 and 74708 is 4.

GCF(74688,74708) = 4

We will now calculate the prime factors of 74688 and 74708, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 74688 and 74708.

How to find the GCF of 74688 and 74708?

We will first find the prime factorization of 74688 and 74708. After we will calculate the factors of 74688 and 74708 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 74708

Prime factors of 74708 are 2, 19, 983. Prime factorization of 74708 in exponential form is:

74708 = 2² × 19¹ × 983¹

Step-3: Factors of 74688

List of positive integer factors of 74688 that divides 74688 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

Step-4: Factors of 74708

List of positive integer factors of 74708 that divides 74688 without a remainder.

1, 2, 4, 19, 38, 76, 983, 1966, 3932, 18677, 37354

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 74688 and 74708. The biggest common factor number is the GCF number.
So the greatest common factor 74688 and 74708 is 4.

Also check out the Least Common Multiple of 74688 and 74708