What is the Greatest Common Factor of 17940 and 17952?

Greatest common factor (GCF) of 17940 and 17952 is 12.

GCF(17940,17952) = 12

We will now calculate the prime factors of 17940 and 17952, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17940 and 17952.

How to find the GCF of 17940 and 17952?

We will first find the prime factorization of 17940 and 17952. After we will calculate the factors of 17940 and 17952 and find the biggest common factor number .

Step-1: Prime Factorization of 17940

Prime factors of 17940 are 2, 3, 5, 13, 23. Prime factorization of 17940 in exponential form is:

17940 = 2² × 3¹ × 5¹ × 13¹ × 23¹

Step-2: Prime Factorization of 17952

Prime factors of 17952 are 2, 3, 11, 17. Prime factorization of 17952 in exponential form is:

17952 = 2⁵ × 3¹ × 11¹ × 17¹

Step-3: Factors of 17940

List of positive integer factors of 17940 that divides 17940 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 13, 15, 20, 23, 26, 30, 39, 46, 52, 60, 65, 69, 78, 92, 115, 130, 138, 156, 195, 230, 260, 276, 299, 345, 390, 460, 598, 690, 780, 897, 1196, 1380, 1495, 1794, 2990, 3588, 4485, 5980, 8970

Step-4: Factors of 17952

List of positive integer factors of 17952 that divides 17940 without a remainder.

1, 2, 3, 4, 6, 8, 11, 12, 16, 17, 22, 24, 32, 33, 34, 44, 48, 51, 66, 68, 88, 96, 102, 132, 136, 176, 187, 204, 264, 272, 352, 374, 408, 528, 544, 561, 748, 816, 1056, 1122, 1496, 1632, 2244, 2992, 4488, 5984, 8976

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17940 and 17952. The biggest common factor number is the GCF number.
So the greatest common factor 17940 and 17952 is 12.

Also check out the Least Common Multiple of 17940 and 17952