What is the Greatest Common Factor of 34272 and 34288?

Greatest common factor (GCF) of 34272 and 34288 is 16.

GCF(34272,34288) = 16

We will now calculate the prime factors of 34272 and 34288, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 34272 and 34288.

How to find the GCF of 34272 and 34288?

We will first find the prime factorization of 34272 and 34288. After we will calculate the factors of 34272 and 34288 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 34288

Prime factors of 34288 are 2, 2143. Prime factorization of 34288 in exponential form is:

34288 = 2⁴ × 2143¹

Step-3: Factors of 34272

List of positive integer factors of 34272 that divides 34272 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

Step-4: Factors of 34288

List of positive integer factors of 34288 that divides 34272 without a remainder.

1, 2, 4, 8, 16, 2143, 4286, 8572, 17144

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 34272 and 34288. The biggest common factor number is the GCF number.
So the greatest common factor 34272 and 34288 is 16.

Also check out the Least Common Multiple of 34272 and 34288