What is the Greatest Common Factor of 72576 and 72590?

Greatest common factor (GCF) of 72576 and 72590 is 14.

GCF(72576,72590) = 14

We will now calculate the prime factors of 72576 and 72590, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 72576 and 72590.

How to find the GCF of 72576 and 72590?

We will first find the prime factorization of 72576 and 72590. After we will calculate the factors of 72576 and 72590 and find the biggest common factor number .

Step-1: Prime Factorization of 72576

Prime factors of 72576 are 2, 3, 7. Prime factorization of 72576 in exponential form is:

72576 = 2⁷ × 3⁴ × 7¹

Step-2: Prime Factorization of 72590

Prime factors of 72590 are 2, 5, 7, 17, 61. Prime factorization of 72590 in exponential form is:

72590 = 2¹ × 5¹ × 7¹ × 17¹ × 61¹

Step-3: Factors of 72576

List of positive integer factors of 72576 that divides 72576 without a remainder.

1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 27, 28, 32, 36, 42, 48, 54, 56, 63, 64, 72, 81, 84, 96, 108, 112, 126, 128, 144, 162, 168, 189, 192, 216, 224, 252, 288, 324, 336, 378, 384, 432, 448, 504, 567, 576, 648, 672, 756, 864, 896, 1008, 1134, 1152, 1296, 1344, 1512, 1728, 2016, 2268, 2592, 2688, 3024, 3456, 4032, 4536, 5184, 6048, 8064, 9072, 10368, 12096, 18144, 24192, 36288

Step-4: Factors of 72590

List of positive integer factors of 72590 that divides 72576 without a remainder.

1, 2, 5, 7, 10, 14, 17, 34, 35, 61, 70, 85, 119, 122, 170, 238, 305, 427, 595, 610, 854, 1037, 1190, 2074, 2135, 4270, 5185, 7259, 10370, 14518, 36295

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 72576 and 72590. The biggest common factor number is the GCF number.
So the greatest common factor 72576 and 72590 is 14.

Also check out the Least Common Multiple of 72576 and 72590