What is the Greatest Common Factor of 5640 and 5649?

Greatest common factor (GCF) of 5640 and 5649 is 3.

GCF(5640,5649) = 3

We will now calculate the prime factors of 5640 and 5649, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 5640 and 5649.

How to find the GCF of 5640 and 5649?

We will first find the prime factorization of 5640 and 5649. After we will calculate the factors of 5640 and 5649 and find the biggest common factor number .

Step-1: Prime Factorization of 5640

Prime factors of 5640 are 2, 3, 5, 47. Prime factorization of 5640 in exponential form is:

5640 = 2³ × 3¹ × 5¹ × 47¹

Step-2: 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-3: Factors of 5640

List of positive integer factors of 5640 that divides 5640 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 47, 60, 94, 120, 141, 188, 235, 282, 376, 470, 564, 705, 940, 1128, 1410, 1880, 2820

Step-4: Factors of 5649

List of positive integer factors of 5649 that divides 5640 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 5640 and 5649. The biggest common factor number is the GCF number.
So the greatest common factor 5640 and 5649 is 3.

Also check out the Least Common Multiple of 5640 and 5649