What is the Greatest Common Factor of 13624 and 13642?

Greatest common factor (GCF) of 13624 and 13642 is 2.

GCF(13624,13642) = 2

We will now calculate the prime factors of 13624 and 13642, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13624 and 13642.

How to find the GCF of 13624 and 13642?

We will first find the prime factorization of 13624 and 13642. After we will calculate the factors of 13624 and 13642 and find the biggest common factor number .

Step-1: Prime Factorization of 13624

Prime factors of 13624 are 2, 13, 131. Prime factorization of 13624 in exponential form is:

13624 = 2³ × 13¹ × 131¹

Step-2: Prime Factorization of 13642

Prime factors of 13642 are 2, 19, 359. Prime factorization of 13642 in exponential form is:

13642 = 2¹ × 19¹ × 359¹

Step-3: Factors of 13624

List of positive integer factors of 13624 that divides 13624 without a remainder.

1, 2, 4, 8, 13, 26, 52, 104, 131, 262, 524, 1048, 1703, 3406, 6812

Step-4: Factors of 13642

List of positive integer factors of 13642 that divides 13624 without a remainder.

1, 2, 19, 38, 359, 718, 6821

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13624 and 13642. The biggest common factor number is the GCF number.
So the greatest common factor 13624 and 13642 is 2.

Also check out the Least Common Multiple of 13624 and 13642