What is the Greatest Common Factor of 17654 and 17672?

Greatest common factor (GCF) of 17654 and 17672 is 2.

GCF(17654,17672) = 2

We will now calculate the prime factors of 17654 and 17672, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17654 and 17672.

How to find the GCF of 17654 and 17672?

We will first find the prime factorization of 17654 and 17672. After we will calculate the factors of 17654 and 17672 and find the biggest common factor number .

Step-1: Prime Factorization of 17654

Prime factors of 17654 are 2, 7, 13, 97. Prime factorization of 17654 in exponential form is:

17654 = 2¹ × 7¹ × 13¹ × 97¹

Step-2: Prime Factorization of 17672

Prime factors of 17672 are 2, 47. Prime factorization of 17672 in exponential form is:

17672 = 2³ × 47²

Step-3: Factors of 17654

List of positive integer factors of 17654 that divides 17654 without a remainder.

1, 2, 7, 13, 14, 26, 91, 97, 182, 194, 679, 1261, 1358, 2522, 8827

Step-4: Factors of 17672

List of positive integer factors of 17672 that divides 17654 without a remainder.

1, 2, 4, 8, 47, 94, 188, 376, 2209, 4418, 8836

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17654 and 17672. The biggest common factor number is the GCF number.
So the greatest common factor 17654 and 17672 is 2.

Also check out the Least Common Multiple of 17654 and 17672