What is the Greatest Common Factor of 74688 and 74704?

Greatest common factor (GCF) of 74688 and 74704 is 16.

GCF(74688,74704) = 16

We will now calculate the prime factors of 74688 and 74704, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 74688 and 74704.

How to find the GCF of 74688 and 74704?

We will first find the prime factorization of 74688 and 74704. After we will calculate the factors of 74688 and 74704 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 74704

Prime factors of 74704 are 2, 7, 23, 29. Prime factorization of 74704 in exponential form is:

74704 = 2⁴ × 7¹ × 23¹ × 29¹

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 74704

List of positive integer factors of 74704 that divides 74688 without a remainder.

1, 2, 4, 7, 8, 14, 16, 23, 28, 29, 46, 56, 58, 92, 112, 116, 161, 184, 203, 232, 322, 368, 406, 464, 644, 667, 812, 1288, 1334, 1624, 2576, 2668, 3248, 4669, 5336, 9338, 10672, 18676, 37352

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 74688 and 74704. The biggest common factor number is the GCF number.
So the greatest common factor 74688 and 74704 is 16.

Also check out the Least Common Multiple of 74688 and 74704