What is the Greatest Common Factor of 59328 and 59346?

Greatest common factor (GCF) of 59328 and 59346 is 18.

GCF(59328,59346) = 18

We will now calculate the prime factors of 59328 and 59346, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 59328 and 59346.

How to find the GCF of 59328 and 59346?

We will first find the prime factorization of 59328 and 59346. After we will calculate the factors of 59328 and 59346 and find the biggest common factor number .

Step-1: Prime Factorization of 59328

Prime factors of 59328 are 2, 3, 103. Prime factorization of 59328 in exponential form is:

59328 = 2⁶ × 3² × 103¹

Step-2: Prime Factorization of 59346

Prime factors of 59346 are 2, 3, 7, 157. Prime factorization of 59346 in exponential form is:

59346 = 2¹ × 3³ × 7¹ × 157¹

Step-3: Factors of 59328

List of positive integer factors of 59328 that divides 59328 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 64, 72, 96, 103, 144, 192, 206, 288, 309, 412, 576, 618, 824, 927, 1236, 1648, 1854, 2472, 3296, 3708, 4944, 6592, 7416, 9888, 14832, 19776, 29664

Step-4: Factors of 59346

List of positive integer factors of 59346 that divides 59328 without a remainder.

1, 2, 3, 6, 7, 9, 14, 18, 21, 27, 42, 54, 63, 126, 157, 189, 314, 378, 471, 942, 1099, 1413, 2198, 2826, 3297, 4239, 6594, 8478, 9891, 19782, 29673

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 59328 and 59346. The biggest common factor number is the GCF number.
So the greatest common factor 59328 and 59346 is 18.

Also check out the Least Common Multiple of 59328 and 59346