What is the Greatest Common Factor of 17712 and 17729?

Greatest common factor (GCF) of 17712 and 17729 is 1.

GCF(17712,17729) = 1

We will now calculate the prime factors of 17712 and 17729, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17712 and 17729.

How to find the GCF of 17712 and 17729?

We will first find the prime factorization of 17712 and 17729. After we will calculate the factors of 17712 and 17729 and find the biggest common factor number .

Step-1: Prime Factorization of 17712

Prime factors of 17712 are 2, 3, 41. Prime factorization of 17712 in exponential form is:

17712 = 2⁴ × 3³ × 41¹

Step-2: Prime Factorization of 17729

Prime factors of 17729 are 17729. Prime factorization of 17729 in exponential form is:

17729 = 17729¹

Step-3: Factors of 17712

List of positive integer factors of 17712 that divides 17712 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 36, 41, 48, 54, 72, 82, 108, 123, 144, 164, 216, 246, 328, 369, 432, 492, 656, 738, 984, 1107, 1476, 1968, 2214, 2952, 4428, 5904, 8856

Step-4: Factors of 17729

List of positive integer factors of 17729 that divides 17712 without a remainder.

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17712 and 17729. The biggest common factor number is the GCF number.
So the greatest common factor 17712 and 17729 is 1.

Also check out the Least Common Multiple of 17712 and 17729