What is the Greatest Common Factor of 17638 and 17648?

Greatest common factor (GCF) of 17638 and 17648 is 2.

GCF(17638,17648) = 2

We will now calculate the prime factors of 17638 and 17648, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17638 and 17648.

How to find the GCF of 17638 and 17648?

We will first find the prime factorization of 17638 and 17648. After we will calculate the factors of 17638 and 17648 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 17648

Prime factors of 17648 are 2, 1103. Prime factorization of 17648 in exponential form is:

17648 = 2⁴ × 1103¹

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 17648

List of positive integer factors of 17648 that divides 17638 without a remainder.

1, 2, 4, 8, 16, 1103, 2206, 4412, 8824

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17638 and 17648. The biggest common factor number is the GCF number.
So the greatest common factor 17638 and 17648 is 2.

Also check out the Least Common Multiple of 17638 and 17648