What is the Greatest Common Factor of 11648 and 11664?

Greatest common factor (GCF) of 11648 and 11664 is 16.

GCF(11648,11664) = 16

We will now calculate the prime factors of 11648 and 11664, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 11648 and 11664.

How to find the GCF of 11648 and 11664?

We will first find the prime factorization of 11648 and 11664. After we will calculate the factors of 11648 and 11664 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 11664

Prime factors of 11664 are 2, 3. Prime factorization of 11664 in exponential form is:

11664 = 2⁴ × 3⁶

Step-3: Factors of 11648

List of positive integer factors of 11648 that divides 11648 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

Step-4: Factors of 11664

List of positive integer factors of 11664 that divides 11648 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 36, 48, 54, 72, 81, 108, 144, 162, 216, 243, 324, 432, 486, 648, 729, 972, 1296, 1458, 1944, 2916, 3888, 5832

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 11648 and 11664. The biggest common factor number is the GCF number.
So the greatest common factor 11648 and 11664 is 16.

Also check out the Least Common Multiple of 11648 and 11664