What is the Greatest Common Factor of 7644 and 7658?

Greatest common factor (GCF) of 7644 and 7658 is 14.

GCF(7644,7658) = 14

We will now calculate the prime factors of 7644 and 7658, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 7644 and 7658.

How to find the GCF of 7644 and 7658?

We will first find the prime factorization of 7644 and 7658. After we will calculate the factors of 7644 and 7658 and find the biggest common factor number .

Step-1: Prime Factorization of 7644

Prime factors of 7644 are 2, 3, 7, 13. Prime factorization of 7644 in exponential form is:

7644 = 2² × 3¹ × 7² × 13¹

Step-2: Prime Factorization of 7658

Prime factors of 7658 are 2, 7, 547. Prime factorization of 7658 in exponential form is:

7658 = 2¹ × 7¹ × 547¹

Step-3: Factors of 7644

List of positive integer factors of 7644 that divides 7644 without a remainder.

1, 2, 3, 4, 6, 7, 12, 13, 14, 21, 26, 28, 39, 42, 49, 52, 78, 84, 91, 98, 147, 156, 182, 196, 273, 294, 364, 546, 588, 637, 1092, 1274, 1911, 2548, 3822

Step-4: Factors of 7658

List of positive integer factors of 7658 that divides 7644 without a remainder.

1, 2, 7, 14, 547, 1094, 3829

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 7644 and 7658. The biggest common factor number is the GCF number.
So the greatest common factor 7644 and 7658 is 14.

Also check out the Least Common Multiple of 7644 and 7658