What is the Greatest Common Factor of 17638 and 17654?

Greatest common factor (GCF) of 17638 and 17654 is 2.

GCF(17638,17654) = 2

We will now calculate the prime factors of 17638 and 17654, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17638 and 17654.

How to find the GCF of 17638 and 17654?

We will first find the prime factorization of 17638 and 17654. After we will calculate the factors of 17638 and 17654 and find the biggest common factor number .

Step-1: Prime Factorization of 17638

Prime factors of 17638 are 2, 8819. Prime factorization of 17638 in exponential form is:

17638 = 2¹ × 8819¹

Step-2: 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-3: Factors of 17638

List of positive integer factors of 17638 that divides 17638 without a remainder.

1, 2, 8819

Step-4: Factors of 17654

List of positive integer factors of 17654 that divides 17638 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17638 and 17654. The biggest common factor number is the GCF number.
So the greatest common factor 17638 and 17654 is 2.

Also check out the Least Common Multiple of 17638 and 17654