What is the Greatest Common Factor of 59280 and 59296?

Greatest common factor (GCF) of 59280 and 59296 is 16.

GCF(59280,59296) = 16

We will now calculate the prime factors of 59280 and 59296, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 59280 and 59296.

How to find the GCF of 59280 and 59296?

We will first find the prime factorization of 59280 and 59296. After we will calculate the factors of 59280 and 59296 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 59296

Prime factors of 59296 are 2, 17, 109. Prime factorization of 59296 in exponential form is:

59296 = 2⁵ × 17¹ × 109¹

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 59296

List of positive integer factors of 59296 that divides 59280 without a remainder.

1, 2, 4, 8, 16, 17, 32, 34, 68, 109, 136, 218, 272, 436, 544, 872, 1744, 1853, 3488, 3706, 7412, 14824, 29648

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 59280 and 59296. The biggest common factor number is the GCF number.
So the greatest common factor 59280 and 59296 is 16.

Also check out the Least Common Multiple of 59280 and 59296