What is the Greatest Common Factor of 59520 and 59538?

Greatest common factor (GCF) of 59520 and 59538 is 6.

GCF(59520,59538) = 6

We will now calculate the prime factors of 59520 and 59538, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 59520 and 59538.

How to find the GCF of 59520 and 59538?

We will first find the prime factorization of 59520 and 59538. After we will calculate the factors of 59520 and 59538 and find the biggest common factor number .

Step-1: Prime Factorization of 59520

Prime factors of 59520 are 2, 3, 5, 31. Prime factorization of 59520 in exponential form is:

59520 = 2⁷ × 3¹ × 5¹ × 31¹

Step-2: Prime Factorization of 59538

Prime factors of 59538 are 2, 3, 9923. Prime factorization of 59538 in exponential form is:

59538 = 2¹ × 3¹ × 9923¹

Step-3: Factors of 59520

List of positive integer factors of 59520 that divides 59520 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 31, 32, 40, 48, 60, 62, 64, 80, 93, 96, 120, 124, 128, 155, 160, 186, 192, 240, 248, 310, 320, 372, 384, 465, 480, 496, 620, 640, 744, 930, 960, 992, 1240, 1488, 1860, 1920, 1984, 2480, 2976, 3720, 3968, 4960, 5952, 7440, 9920, 11904, 14880, 19840, 29760

Step-4: Factors of 59538

List of positive integer factors of 59538 that divides 59520 without a remainder.

1, 2, 3, 6, 9923, 19846, 29769

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 59520 and 59538. The biggest common factor number is the GCF number.
So the greatest common factor 59520 and 59538 is 6.

Also check out the Least Common Multiple of 59520 and 59538