What is the Greatest Common Factor of 11634 and 11648?

Greatest common factor (GCF) of 11634 and 11648 is 14.

GCF(11634,11648) = 14

We will now calculate the prime factors of 11634 and 11648, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 11634 and 11648.

How to find the GCF of 11634 and 11648?

We will first find the prime factorization of 11634 and 11648. After we will calculate the factors of 11634 and 11648 and find the biggest common factor number .

Step-1: Prime Factorization of 11634

Prime factors of 11634 are 2, 3, 7, 277. Prime factorization of 11634 in exponential form is:

11634 = 2¹ × 3¹ × 7¹ × 277¹

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 11634

List of positive integer factors of 11634 that divides 11634 without a remainder.

1, 2, 3, 6, 7, 14, 21, 42, 277, 554, 831, 1662, 1939, 3878, 5817

Step-4: Factors of 11648

List of positive integer factors of 11648 that divides 11634 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 11634 and 11648. The biggest common factor number is the GCF number.
So the greatest common factor 11634 and 11648 is 14.

Also check out the Least Common Multiple of 11634 and 11648