What is the Greatest Common Factor of 34128 and 34144?

Greatest common factor (GCF) of 34128 and 34144 is 16.

GCF(34128,34144) = 16

We will now calculate the prime factors of 34128 and 34144, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 34128 and 34144.

How to find the GCF of 34128 and 34144?

We will first find the prime factorization of 34128 and 34144. After we will calculate the factors of 34128 and 34144 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 34144

Prime factors of 34144 are 2, 11, 97. Prime factorization of 34144 in exponential form is:

34144 = 2⁵ × 11¹ × 97¹

Step-3: Factors of 34128

List of positive integer factors of 34128 that divides 34128 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

Step-4: Factors of 34144

List of positive integer factors of 34144 that divides 34128 without a remainder.

1, 2, 4, 8, 11, 16, 22, 32, 44, 88, 97, 176, 194, 352, 388, 776, 1067, 1552, 2134, 3104, 4268, 8536, 17072

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 34128 and 34144. The biggest common factor number is the GCF number.
So the greatest common factor 34128 and 34144 is 16.

Also check out the Least Common Multiple of 34128 and 34144