What is the Greatest Common Factor of 17952 and 17970?

Greatest common factor (GCF) of 17952 and 17970 is 6.

GCF(17952,17970) = 6

We will now calculate the prime factors of 17952 and 17970, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17952 and 17970.

How to find the GCF of 17952 and 17970?

We will first find the prime factorization of 17952 and 17970. After we will calculate the factors of 17952 and 17970 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 17970

Prime factors of 17970 are 2, 3, 5, 599. Prime factorization of 17970 in exponential form is:

17970 = 2¹ × 3¹ × 5¹ × 599¹

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 17970

List of positive integer factors of 17970 that divides 17952 without a remainder.

1, 2, 3, 5, 6, 10, 15, 30, 599, 1198, 1797, 2995, 3594, 5990, 8985

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17952 and 17970. The biggest common factor number is the GCF number.
So the greatest common factor 17952 and 17970 is 6.

Also check out the Least Common Multiple of 17952 and 17970