What is the Greatest Common Factor of 11638 and 11648?

Greatest common factor (GCF) of 11638 and 11648 is 2.

GCF(11638,11648) = 2

We will now calculate the prime factors of 11638 and 11648, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 11638 and 11648.

How to find the GCF of 11638 and 11648?

We will first find the prime factorization of 11638 and 11648. After we will calculate the factors of 11638 and 11648 and find the biggest common factor number .

Step-1: Prime Factorization of 11638

Prime factors of 11638 are 2, 11, 23. Prime factorization of 11638 in exponential form is:

11638 = 2¹ × 11¹ × 23²

Step-2: Prime Factorization of 11648

Prime factors of 11648 are 2, 7, 13. Prime factorization of 11648 in exponential form is:

11648 = 2⁷ × 7¹ × 13¹

Step-3: Factors of 11638

List of positive integer factors of 11638 that divides 11638 without a remainder.

1, 2, 11, 22, 23, 46, 253, 506, 529, 1058, 5819

Step-4: Factors of 11648

List of positive integer factors of 11648 that divides 11638 without a remainder.

1, 2, 4, 7, 8, 13, 14, 16, 26, 28, 32, 52, 56, 64, 91, 104, 112, 128, 182, 208, 224, 364, 416, 448, 728, 832, 896, 1456, 1664, 2912, 5824

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 11638 and 11648. The biggest common factor number is the GCF number.
So the greatest common factor 11638 and 11648 is 2.

Also check out the Least Common Multiple of 11638 and 11648