What is the Greatest Common Factor of 7630 and 7644?

Greatest common factor (GCF) of 7630 and 7644 is 14.

GCF(7630,7644) = 14

We will now calculate the prime factors of 7630 and 7644, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 7630 and 7644.

How to find the GCF of 7630 and 7644?

We will first find the prime factorization of 7630 and 7644. After we will calculate the factors of 7630 and 7644 and find the biggest common factor number .

Step-1: Prime Factorization of 7630

Prime factors of 7630 are 2, 5, 7, 109. Prime factorization of 7630 in exponential form is:

7630 = 2¹ × 5¹ × 7¹ × 109¹

Step-2: 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-3: Factors of 7630

List of positive integer factors of 7630 that divides 7630 without a remainder.

1, 2, 5, 7, 10, 14, 35, 70, 109, 218, 545, 763, 1090, 1526, 3815

Step-4: Factors of 7644

List of positive integer factors of 7644 that divides 7630 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 7630 and 7644. The biggest common factor number is the GCF number.
So the greatest common factor 7630 and 7644 is 14.

Also check out the Least Common Multiple of 7630 and 7644