What is the Greatest Common Factor of 17460 and 17472?

Greatest common factor (GCF) of 17460 and 17472 is 12.

GCF(17460,17472) = 12

We will now calculate the prime factors of 17460 and 17472, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17460 and 17472.

How to find the GCF of 17460 and 17472?

We will first find the prime factorization of 17460 and 17472. After we will calculate the factors of 17460 and 17472 and find the biggest common factor number .

Step-1: Prime Factorization of 17460

Prime factors of 17460 are 2, 3, 5, 97. Prime factorization of 17460 in exponential form is:

17460 = 2² × 3² × 5¹ × 97¹

Step-2: Prime Factorization of 17472

Prime factors of 17472 are 2, 3, 7, 13. Prime factorization of 17472 in exponential form is:

17472 = 2⁶ × 3¹ × 7¹ × 13¹

Step-3: Factors of 17460

List of positive integer factors of 17460 that divides 17460 without a remainder.

1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 97, 180, 194, 291, 388, 485, 582, 873, 970, 1164, 1455, 1746, 1940, 2910, 3492, 4365, 5820, 8730

Step-4: Factors of 17472

List of positive integer factors of 17472 that divides 17460 without a remainder.

1, 2, 3, 4, 6, 7, 8, 12, 13, 14, 16, 21, 24, 26, 28, 32, 39, 42, 48, 52, 56, 64, 78, 84, 91, 96, 104, 112, 156, 168, 182, 192, 208, 224, 273, 312, 336, 364, 416, 448, 546, 624, 672, 728, 832, 1092, 1248, 1344, 1456, 2184, 2496, 2912, 4368, 5824, 8736

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17460 and 17472. The biggest common factor number is the GCF number.
So the greatest common factor 17460 and 17472 is 12.

Also check out the Least Common Multiple of 17460 and 17472