What is the Greatest Common Factor of 34254 and 34272?

Greatest common factor (GCF) of 34254 and 34272 is 18.

GCF(34254,34272) = 18

We will now calculate the prime factors of 34254 and 34272, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 34254 and 34272.

How to find the GCF of 34254 and 34272?

We will first find the prime factorization of 34254 and 34272. After we will calculate the factors of 34254 and 34272 and find the biggest common factor number .

Step-1: Prime Factorization of 34254

Prime factors of 34254 are 2, 3, 11, 173. Prime factorization of 34254 in exponential form is:

34254 = 2¹ × 3² × 11¹ × 173¹

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 34254

List of positive integer factors of 34254 that divides 34254 without a remainder.

1, 2, 3, 6, 9, 11, 18, 22, 33, 66, 99, 173, 198, 346, 519, 1038, 1557, 1903, 3114, 3806, 5709, 11418, 17127

Step-4: Factors of 34272

List of positive integer factors of 34272 that divides 34254 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 34254 and 34272. The biggest common factor number is the GCF number.
So the greatest common factor 34254 and 34272 is 18.

Also check out the Least Common Multiple of 34254 and 34272