What is the Greatest Common Factor of 59280 and 59295?

Greatest common factor (GCF) of 59280 and 59295 is 15.

GCF(59280,59295) = 15

We will now calculate the prime factors of 59280 and 59295, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 59280 and 59295.

How to find the GCF of 59280 and 59295?

We will first find the prime factorization of 59280 and 59295. After we will calculate the factors of 59280 and 59295 and find the biggest common factor number .

Step-1: Prime Factorization of 59280

Prime factors of 59280 are 2, 3, 5, 13, 19. Prime factorization of 59280 in exponential form is:

59280 = 2⁴ × 3¹ × 5¹ × 13¹ × 19¹

Step-2: Prime Factorization of 59295

Prime factors of 59295 are 3, 5, 59, 67. Prime factorization of 59295 in exponential form is:

59295 = 3¹ × 5¹ × 59¹ × 67¹

Step-3: Factors of 59280

List of positive integer factors of 59280 that divides 59280 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 13, 15, 16, 19, 20, 24, 26, 30, 38, 39, 40, 48, 52, 57, 60, 65, 76, 78, 80, 95, 104, 114, 120, 130, 152, 156, 190, 195, 208, 228, 240, 247, 260, 285, 304, 312, 380, 390, 456, 494, 520, 570, 624, 741, 760, 780, 912, 988, 1040, 1140, 1235, 1482, 1520, 1560, 1976, 2280, 2470, 2964, 3120, 3705, 3952, 4560, 4940, 5928, 7410, 9880, 11856, 14820, 19760, 29640

Step-4: Factors of 59295

List of positive integer factors of 59295 that divides 59280 without a remainder.

1, 3, 5, 15, 59, 67, 177, 201, 295, 335, 885, 1005, 3953, 11859, 19765

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 59280 and 59295. The biggest common factor number is the GCF number.
So the greatest common factor 59280 and 59295 is 15.

Also check out the Least Common Multiple of 59280 and 59295