What is the Greatest Common Factor of 34944 and 34952?

Greatest common factor (GCF) of 34944 and 34952 is 8.

GCF(34944,34952) = 8

We will now calculate the prime factors of 34944 and 34952, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 34944 and 34952.

How to find the GCF of 34944 and 34952?

We will first find the prime factorization of 34944 and 34952. After we will calculate the factors of 34944 and 34952 and find the biggest common factor number .

Step-1: Prime Factorization of 34944

Prime factors of 34944 are 2, 3, 7, 13. Prime factorization of 34944 in exponential form is:

34944 = 2⁷ × 3¹ × 7¹ × 13¹

Step-2: Prime Factorization of 34952

Prime factors of 34952 are 2, 17, 257. Prime factorization of 34952 in exponential form is:

34952 = 2³ × 17¹ × 257¹

Step-3: Factors of 34944

List of positive integer factors of 34944 that divides 34944 without a remainder.

1, 2, 3, 4, 6, 7, 8, 12, 13, 14, 16, 21, 24, 26, 28, 32, 39, 42, 48, 52, 56, 64, 78, 84, 91, 96, 104, 112, 128, 156, 168, 182, 192, 208, 224, 273, 312, 336, 364, 384, 416, 448, 546, 624, 672, 728, 832, 896, 1092, 1248, 1344, 1456, 1664, 2184, 2496, 2688, 2912, 4368, 4992, 5824, 8736, 11648, 17472

Step-4: Factors of 34952

List of positive integer factors of 34952 that divides 34944 without a remainder.

1, 2, 4, 8, 17, 34, 68, 136, 257, 514, 1028, 2056, 4369, 8738, 17476

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 34944 and 34952. The biggest common factor number is the GCF number.
So the greatest common factor 34944 and 34952 is 8.

Also check out the Least Common Multiple of 34944 and 34952