What is the Greatest Common Factor of 34935 and 34944?

Greatest common factor (GCF) of 34935 and 34944 is 3.

GCF(34935,34944) = 3

We will now calculate the prime factors of 34935 and 34944, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 34935 and 34944.

How to find the GCF of 34935 and 34944?

We will first find the prime factorization of 34935 and 34944. After we will calculate the factors of 34935 and 34944 and find the biggest common factor number .

Step-1: Prime Factorization of 34935

Prime factors of 34935 are 3, 5, 17, 137. Prime factorization of 34935 in exponential form is:

34935 = 3¹ × 5¹ × 17¹ × 137¹

Step-2: 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-3: Factors of 34935

List of positive integer factors of 34935 that divides 34935 without a remainder.

1, 3, 5, 15, 17, 51, 85, 137, 255, 411, 685, 2055, 2329, 6987, 11645

Step-4: Factors of 34944

List of positive integer factors of 34944 that divides 34935 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 34935 and 34944. The biggest common factor number is the GCF number.
So the greatest common factor 34935 and 34944 is 3.

Also check out the Least Common Multiple of 34935 and 34944