What is the Greatest Common Factor of 5649 and 5664?

Greatest common factor (GCF) of 5649 and 5664 is 3.

GCF(5649,5664) = 3

We will now calculate the prime factors of 5649 and 5664, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 5649 and 5664.

How to find the GCF of 5649 and 5664?

We will first find the prime factorization of 5649 and 5664. After we will calculate the factors of 5649 and 5664 and find the biggest common factor number .

Step-1: Prime Factorization of 5649

Prime factors of 5649 are 3, 7, 269. Prime factorization of 5649 in exponential form is:

5649 = 3¹ × 7¹ × 269¹

Step-2: Prime Factorization of 5664

Prime factors of 5664 are 2, 3, 59. Prime factorization of 5664 in exponential form is:

5664 = 2⁵ × 3¹ × 59¹

Step-3: Factors of 5649

List of positive integer factors of 5649 that divides 5649 without a remainder.

1, 3, 7, 21, 269, 807, 1883

Step-4: Factors of 5664

List of positive integer factors of 5664 that divides 5649 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 59, 96, 118, 177, 236, 354, 472, 708, 944, 1416, 1888, 2832

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 5649 and 5664. The biggest common factor number is the GCF number.
So the greatest common factor 5649 and 5664 is 3.

Also check out the Least Common Multiple of 5649 and 5664