What is the Greatest Common Factor of 34256 and 34272?

Greatest common factor (GCF) of 34256 and 34272 is 16.

GCF(34256,34272) = 16

We will now calculate the prime factors of 34256 and 34272, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 34256 and 34272.

How to find the GCF of 34256 and 34272?

We will first find the prime factorization of 34256 and 34272. After we will calculate the factors of 34256 and 34272 and find the biggest common factor number .

Step-1: Prime Factorization of 34256

Prime factors of 34256 are 2, 2141. Prime factorization of 34256 in exponential form is:

34256 = 2⁴ × 2141¹

Step-2: Prime Factorization of 34272

Prime factors of 34272 are 2, 3, 7, 17. Prime factorization of 34272 in exponential form is:

34272 = 2⁵ × 3² × 7¹ × 17¹

Step-3: Factors of 34256

List of positive integer factors of 34256 that divides 34256 without a remainder.

1, 2, 4, 8, 16, 2141, 4282, 8564, 17128

Step-4: Factors of 34272

List of positive integer factors of 34272 that divides 34256 without a remainder.

1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 17, 18, 21, 24, 28, 32, 34, 36, 42, 48, 51, 56, 63, 68, 72, 84, 96, 102, 112, 119, 126, 136, 144, 153, 168, 204, 224, 238, 252, 272, 288, 306, 336, 357, 408, 476, 504, 544, 612, 672, 714, 816, 952, 1008, 1071, 1224, 1428, 1632, 1904, 2016, 2142, 2448, 2856, 3808, 4284, 4896, 5712, 8568, 11424, 17136

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 34256 and 34272. The biggest common factor number is the GCF number.
So the greatest common factor 34256 and 34272 is 16.

Also check out the Least Common Multiple of 34256 and 34272