What is the Greatest Common Factor of 17952 and 17969?

Greatest common factor (GCF) of 17952 and 17969 is 17.

GCF(17952,17969) = 17

We will now calculate the prime factors of 17952 and 17969, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17952 and 17969.

How to find the GCF of 17952 and 17969?

We will first find the prime factorization of 17952 and 17969. After we will calculate the factors of 17952 and 17969 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 17969

Prime factors of 17969 are 7, 17, 151. Prime factorization of 17969 in exponential form is:

17969 = 7¹ × 17¹ × 151¹

Step-3: Factors of 17952

List of positive integer factors of 17952 that divides 17952 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

Step-4: Factors of 17969

List of positive integer factors of 17969 that divides 17952 without a remainder.

1, 7, 17, 119, 151, 1057, 2567

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17952 and 17969. The biggest common factor number is the GCF number.
So the greatest common factor 17952 and 17969 is 17.

Also check out the Least Common Multiple of 17952 and 17969