What is the Greatest Common Factor of 74112 and 74128?

Greatest common factor (GCF) of 74112 and 74128 is 16.

GCF(74112,74128) = 16

We will now calculate the prime factors of 74112 and 74128, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 74112 and 74128.

How to find the GCF of 74112 and 74128?

We will first find the prime factorization of 74112 and 74128. After we will calculate the factors of 74112 and 74128 and find the biggest common factor number .

Step-1: Prime Factorization of 74112

Prime factors of 74112 are 2, 3, 193. Prime factorization of 74112 in exponential form is:

74112 = 2⁷ × 3¹ × 193¹

Step-2: Prime Factorization of 74128

Prime factors of 74128 are 2, 41, 113. Prime factorization of 74128 in exponential form is:

74128 = 2⁴ × 41¹ × 113¹

Step-3: Factors of 74112

List of positive integer factors of 74112 that divides 74112 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 193, 384, 386, 579, 772, 1158, 1544, 2316, 3088, 4632, 6176, 9264, 12352, 18528, 24704, 37056

Step-4: Factors of 74128

List of positive integer factors of 74128 that divides 74112 without a remainder.

1, 2, 4, 8, 16, 41, 82, 113, 164, 226, 328, 452, 656, 904, 1808, 4633, 9266, 18532, 37064

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 74112 and 74128. The biggest common factor number is the GCF number.
So the greatest common factor 74112 and 74128 is 16.

Also check out the Least Common Multiple of 74112 and 74128