What is the Greatest Common Factor of 13634 and 13640?

Greatest common factor (GCF) of 13634 and 13640 is 2.

GCF(13634,13640) = 2

We will now calculate the prime factors of 13634 and 13640, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13634 and 13640.

How to find the GCF of 13634 and 13640?

We will first find the prime factorization of 13634 and 13640. After we will calculate the factors of 13634 and 13640 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 13640

Prime factors of 13640 are 2, 5, 11, 31. Prime factorization of 13640 in exponential form is:

13640 = 2³ × 5¹ × 11¹ × 31¹

Step-3: Factors of 13634

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

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

Step-4: Factors of 13640

List of positive integer factors of 13640 that divides 13634 without a remainder.

1, 2, 4, 5, 8, 10, 11, 20, 22, 31, 40, 44, 55, 62, 88, 110, 124, 155, 220, 248, 310, 341, 440, 620, 682, 1240, 1364, 1705, 2728, 3410, 6820

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13634 and 13640. The biggest common factor number is the GCF number.
So the greatest common factor 13634 and 13640 is 2.

Also check out the Least Common Multiple of 13634 and 13640