What is the Greatest Common Factor of 34112 and 34128?

Greatest common factor (GCF) of 34112 and 34128 is 16.

GCF(34112,34128) = 16

We will now calculate the prime factors of 34112 and 34128, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 34112 and 34128.

How to find the GCF of 34112 and 34128?

We will first find the prime factorization of 34112 and 34128. After we will calculate the factors of 34112 and 34128 and find the biggest common factor number .

Step-1: Prime Factorization of 34112

Prime factors of 34112 are 2, 13, 41. Prime factorization of 34112 in exponential form is:

34112 = 2⁶ × 13¹ × 41¹

Step-2: Prime Factorization of 34128

Prime factors of 34128 are 2, 3, 79. Prime factorization of 34128 in exponential form is:

34128 = 2⁴ × 3³ × 79¹

Step-3: Factors of 34112

List of positive integer factors of 34112 that divides 34112 without a remainder.

1, 2, 4, 8, 13, 16, 26, 32, 41, 52, 64, 82, 104, 164, 208, 328, 416, 533, 656, 832, 1066, 1312, 2132, 2624, 4264, 8528, 17056

Step-4: Factors of 34128

List of positive integer factors of 34128 that divides 34112 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 36, 48, 54, 72, 79, 108, 144, 158, 216, 237, 316, 432, 474, 632, 711, 948, 1264, 1422, 1896, 2133, 2844, 3792, 4266, 5688, 8532, 11376, 17064

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 34112 and 34128. The biggest common factor number is the GCF number.
So the greatest common factor 34112 and 34128 is 16.

Also check out the Least Common Multiple of 34112 and 34128