What is the Greatest Common Factor of 17952 and 17972?

Greatest common factor (GCF) of 17952 and 17972 is 4.

GCF(17952,17972) = 4

We will now calculate the prime factors of 17952 and 17972, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17952 and 17972.

How to find the GCF of 17952 and 17972?

We will first find the prime factorization of 17952 and 17972. After we will calculate the factors of 17952 and 17972 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 17972

Prime factors of 17972 are 2, 4493. Prime factorization of 17972 in exponential form is:

17972 = 2² × 4493¹

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 17972

List of positive integer factors of 17972 that divides 17952 without a remainder.

1, 2, 4, 4493, 8986

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17952 and 17972. The biggest common factor number is the GCF number.
So the greatest common factor 17952 and 17972 is 4.

Also check out the Least Common Multiple of 17952 and 17972