What is the Greatest Common Factor of 17946 and 17952?

Greatest common factor (GCF) of 17946 and 17952 is 6.

GCF(17946,17952) = 6

We will now calculate the prime factors of 17946 and 17952, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17946 and 17952.

How to find the GCF of 17946 and 17952?

We will first find the prime factorization of 17946 and 17952. After we will calculate the factors of 17946 and 17952 and find the biggest common factor number .

Step-1: Prime Factorization of 17946

Prime factors of 17946 are 2, 3, 997. Prime factorization of 17946 in exponential form is:

17946 = 2¹ × 3² × 997¹

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 17946

List of positive integer factors of 17946 that divides 17946 without a remainder.

1, 2, 3, 6, 9, 18, 997, 1994, 2991, 5982, 8973

Step-4: Factors of 17952

List of positive integer factors of 17952 that divides 17946 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 17946 and 17952. The biggest common factor number is the GCF number.
So the greatest common factor 17946 and 17952 is 6.

Also check out the Least Common Multiple of 17946 and 17952