What is the Greatest Common Factor of 54642 and 54656?

Greatest common factor (GCF) of 54642 and 54656 is 14.

GCF(54642,54656) = 14

We will now calculate the prime factors of 54642 and 54656, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 54642 and 54656.

How to find the GCF of 54642 and 54656?

We will first find the prime factorization of 54642 and 54656. After we will calculate the factors of 54642 and 54656 and find the biggest common factor number .

Step-1: Prime Factorization of 54642

Prime factors of 54642 are 2, 3, 7, 1301. Prime factorization of 54642 in exponential form is:

54642 = 2¹ × 3¹ × 7¹ × 1301¹

Step-2: Prime Factorization of 54656

Prime factors of 54656 are 2, 7, 61. Prime factorization of 54656 in exponential form is:

54656 = 2⁷ × 7¹ × 61¹

Step-3: Factors of 54642

List of positive integer factors of 54642 that divides 54642 without a remainder.

1, 2, 3, 6, 7, 14, 21, 42, 1301, 2602, 3903, 7806, 9107, 18214, 27321

Step-4: Factors of 54656

List of positive integer factors of 54656 that divides 54642 without a remainder.

1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 61, 64, 112, 122, 128, 224, 244, 427, 448, 488, 854, 896, 976, 1708, 1952, 3416, 3904, 6832, 7808, 13664, 27328

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 54642 and 54656. The biggest common factor number is the GCF number.
So the greatest common factor 54642 and 54656 is 14.

Also check out the Least Common Multiple of 54642 and 54656