What is the Greatest Common Factor of 54509 and 54516?

Greatest common factor (GCF) of 54509 and 54516 is 7.

GCF(54509,54516) = 7

We will now calculate the prime factors of 54509 and 54516, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 54509 and 54516.

How to find the GCF of 54509 and 54516?

We will first find the prime factorization of 54509 and 54516. After we will calculate the factors of 54509 and 54516 and find the biggest common factor number .

Step-1: Prime Factorization of 54509

Prime factors of 54509 are 7, 13, 599. Prime factorization of 54509 in exponential form is:

54509 = 7¹ × 13¹ × 599¹

Step-2: Prime Factorization of 54516

Prime factors of 54516 are 2, 3, 7, 11, 59. Prime factorization of 54516 in exponential form is:

54516 = 2² × 3¹ × 7¹ × 11¹ × 59¹

Step-3: Factors of 54509

List of positive integer factors of 54509 that divides 54509 without a remainder.

1, 7, 13, 91, 599, 4193, 7787

Step-4: Factors of 54516

List of positive integer factors of 54516 that divides 54509 without a remainder.

1, 2, 3, 4, 6, 7, 11, 12, 14, 21, 22, 28, 33, 42, 44, 59, 66, 77, 84, 118, 132, 154, 177, 231, 236, 308, 354, 413, 462, 649, 708, 826, 924, 1239, 1298, 1652, 1947, 2478, 2596, 3894, 4543, 4956, 7788, 9086, 13629, 18172, 27258

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 54509 and 54516. The biggest common factor number is the GCF number.
So the greatest common factor 54509 and 54516 is 7.

Also check out the Least Common Multiple of 54509 and 54516