What is the Greatest Common Factor of 17630 and 17648?

Greatest common factor (GCF) of 17630 and 17648 is 2.

GCF(17630,17648) = 2

We will now calculate the prime factors of 17630 and 17648, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17630 and 17648.

How to find the GCF of 17630 and 17648?

We will first find the prime factorization of 17630 and 17648. After we will calculate the factors of 17630 and 17648 and find the biggest common factor number .

Step-1: Prime Factorization of 17630

Prime factors of 17630 are 2, 5, 41, 43. Prime factorization of 17630 in exponential form is:

17630 = 2¹ × 5¹ × 41¹ × 43¹

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 17630

List of positive integer factors of 17630 that divides 17630 without a remainder.

1, 2, 5, 10, 41, 43, 82, 86, 205, 215, 410, 430, 1763, 3526, 8815

Step-4: Factors of 17648

List of positive integer factors of 17648 that divides 17630 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 17630 and 17648. The biggest common factor number is the GCF number.
So the greatest common factor 17630 and 17648 is 2.

Also check out the Least Common Multiple of 17630 and 17648