What is the Greatest Common Factor of 34944 and 34953?

Greatest common factor (GCF) of 34944 and 34953 is 3.

GCF(34944,34953) = 3

We will now calculate the prime factors of 34944 and 34953, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 34944 and 34953.

How to find the GCF of 34944 and 34953?

We will first find the prime factorization of 34944 and 34953. After we will calculate the factors of 34944 and 34953 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 34953

Prime factors of 34953 are 3, 61, 191. Prime factorization of 34953 in exponential form is:

34953 = 3¹ × 61¹ × 191¹

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 34953

List of positive integer factors of 34953 that divides 34944 without a remainder.

1, 3, 61, 183, 191, 573, 11651

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 34944 and 34953. The biggest common factor number is the GCF number.
So the greatest common factor 34944 and 34953 is 3.

Also check out the Least Common Multiple of 34944 and 34953