What is the Greatest Common Factor of 13616 and 13634?

Greatest common factor (GCF) of 13616 and 13634 is 2.

GCF(13616,13634) = 2

We will now calculate the prime factors of 13616 and 13634, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13616 and 13634.

How to find the GCF of 13616 and 13634?

We will first find the prime factorization of 13616 and 13634. After we will calculate the factors of 13616 and 13634 and find the biggest common factor number .

Step-1: Prime Factorization of 13616

Prime factors of 13616 are 2, 23, 37. Prime factorization of 13616 in exponential form is:

13616 = 2⁴ × 23¹ × 37¹

Step-2: Prime Factorization of 13634

Prime factors of 13634 are 2, 17, 401. Prime factorization of 13634 in exponential form is:

13634 = 2¹ × 17¹ × 401¹

Step-3: Factors of 13616

List of positive integer factors of 13616 that divides 13616 without a remainder.

1, 2, 4, 8, 16, 23, 37, 46, 74, 92, 148, 184, 296, 368, 592, 851, 1702, 3404, 6808

Step-4: Factors of 13634

List of positive integer factors of 13634 that divides 13616 without a remainder.

1, 2, 17, 34, 401, 802, 6817

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13616 and 13634. The biggest common factor number is the GCF number.
So the greatest common factor 13616 and 13634 is 2.

Also check out the Least Common Multiple of 13616 and 13634