What is the Greatest Common Factor of 13634 and 13650?

Greatest common factor (GCF) of 13634 and 13650 is 2.

GCF(13634,13650) = 2

We will now calculate the prime factors of 13634 and 13650, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13634 and 13650.

How to find the GCF of 13634 and 13650?

We will first find the prime factorization of 13634 and 13650. After we will calculate the factors of 13634 and 13650 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 13650

Prime factors of 13650 are 2, 3, 5, 7, 13. Prime factorization of 13650 in exponential form is:

13650 = 2¹ × 3¹ × 5² × 7¹ × 13¹

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 13650

List of positive integer factors of 13650 that divides 13634 without a remainder.

1, 2, 3, 5, 6, 7, 10, 13, 14, 15, 21, 25, 26, 30, 35, 39, 42, 50, 65, 70, 75, 78, 91, 105, 130, 150, 175, 182, 195, 210, 273, 325, 350, 390, 455, 525, 546, 650, 910, 975, 1050, 1365, 1950, 2275, 2730, 4550, 6825

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13634 and 13650. The biggest common factor number is the GCF number.
So the greatest common factor 13634 and 13650 is 2.

Also check out the Least Common Multiple of 13634 and 13650