What is the Greatest Common Factor of 59505 and 59520?

Greatest common factor (GCF) of 59505 and 59520 is 15.

GCF(59505,59520) = 15

We will now calculate the prime factors of 59505 and 59520, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 59505 and 59520.

How to find the GCF of 59505 and 59520?

We will first find the prime factorization of 59505 and 59520. After we will calculate the factors of 59505 and 59520 and find the biggest common factor number .

Step-1: Prime Factorization of 59505

Prime factors of 59505 are 3, 5, 3967. Prime factorization of 59505 in exponential form is:

59505 = 3¹ × 5¹ × 3967¹

Step-2: 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-3: Factors of 59505

List of positive integer factors of 59505 that divides 59505 without a remainder.

1, 3, 5, 15, 3967, 11901, 19835

Step-4: Factors of 59520

List of positive integer factors of 59520 that divides 59505 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 59505 and 59520. The biggest common factor number is the GCF number.
So the greatest common factor 59505 and 59520 is 15.

Also check out the Least Common Multiple of 59505 and 59520