What is the Greatest Common Factor of 74613 and 74624?

Greatest common factor (GCF) of 74613 and 74624 is 11.

GCF(74613,74624) = 11

We will now calculate the prime factors of 74613 and 74624, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 74613 and 74624.

How to find the GCF of 74613 and 74624?

We will first find the prime factorization of 74613 and 74624. After we will calculate the factors of 74613 and 74624 and find the biggest common factor number .

Step-1: Prime Factorization of 74613

Prime factors of 74613 are 3, 7, 11, 17, 19. Prime factorization of 74613 in exponential form is:

74613 = 3¹ × 7¹ × 11¹ × 17¹ × 19¹

Step-2: Prime Factorization of 74624

Prime factors of 74624 are 2, 11, 53. Prime factorization of 74624 in exponential form is:

74624 = 2⁷ × 11¹ × 53¹

Step-3: Factors of 74613

List of positive integer factors of 74613 that divides 74613 without a remainder.

1, 3, 7, 11, 17, 19, 21, 33, 51, 57, 77, 119, 133, 187, 209, 231, 323, 357, 399, 561, 627, 969, 1309, 1463, 2261, 3553, 3927, 4389, 6783, 10659, 24871

Step-4: Factors of 74624

List of positive integer factors of 74624 that divides 74613 without a remainder.

1, 2, 4, 8, 11, 16, 22, 32, 44, 53, 64, 88, 106, 128, 176, 212, 352, 424, 583, 704, 848, 1166, 1408, 1696, 2332, 3392, 4664, 6784, 9328, 18656, 37312

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 74613 and 74624. The biggest common factor number is the GCF number.
So the greatest common factor 74613 and 74624 is 11.

Also check out the Least Common Multiple of 74613 and 74624