What is the Greatest Common Factor of 17644 and 17658?

Greatest common factor (GCF) of 17644 and 17658 is 2.

GCF(17644,17658) = 2

We will now calculate the prime factors of 17644 and 17658, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17644 and 17658.

How to find the GCF of 17644 and 17658?

We will first find the prime factorization of 17644 and 17658. After we will calculate the factors of 17644 and 17658 and find the biggest common factor number .

Step-1: Prime Factorization of 17644

Prime factors of 17644 are 2, 11, 401. Prime factorization of 17644 in exponential form is:

17644 = 2² × 11¹ × 401¹

Step-2: Prime Factorization of 17658

Prime factors of 17658 are 2, 3, 109. Prime factorization of 17658 in exponential form is:

17658 = 2¹ × 3⁴ × 109¹

Step-3: Factors of 17644

List of positive integer factors of 17644 that divides 17644 without a remainder.

1, 2, 4, 11, 22, 44, 401, 802, 1604, 4411, 8822

Step-4: Factors of 17658

List of positive integer factors of 17658 that divides 17644 without a remainder.

1, 2, 3, 6, 9, 18, 27, 54, 81, 109, 162, 218, 327, 654, 981, 1962, 2943, 5886, 8829

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17644 and 17658. The biggest common factor number is the GCF number.
So the greatest common factor 17644 and 17658 is 2.

Also check out the Least Common Multiple of 17644 and 17658