What is the Greatest Common Factor of 7638 and 7656?

Greatest common factor (GCF) of 7638 and 7656 is 6.

GCF(7638,7656) = 6

We will now calculate the prime factors of 7638 and 7656, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 7638 and 7656.

How to find the GCF of 7638 and 7656?

We will first find the prime factorization of 7638 and 7656. After we will calculate the factors of 7638 and 7656 and find the biggest common factor number .

Step-1: Prime Factorization of 7638

Prime factors of 7638 are 2, 3, 19, 67. Prime factorization of 7638 in exponential form is:

7638 = 2¹ × 3¹ × 19¹ × 67¹

Step-2: Prime Factorization of 7656

Prime factors of 7656 are 2, 3, 11, 29. Prime factorization of 7656 in exponential form is:

7656 = 2³ × 3¹ × 11¹ × 29¹

Step-3: Factors of 7638

List of positive integer factors of 7638 that divides 7638 without a remainder.

1, 2, 3, 6, 19, 38, 57, 67, 114, 134, 201, 402, 1273, 2546, 3819

Step-4: Factors of 7656

List of positive integer factors of 7656 that divides 7638 without a remainder.

1, 2, 3, 4, 6, 8, 11, 12, 22, 24, 29, 33, 44, 58, 66, 87, 88, 116, 132, 174, 232, 264, 319, 348, 638, 696, 957, 1276, 1914, 2552, 3828

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 7638 and 7656. The biggest common factor number is the GCF number.
So the greatest common factor 7638 and 7656 is 6.

Also check out the Least Common Multiple of 7638 and 7656