What is the Greatest Common Factor of 5670 and 5684?

Greatest common factor (GCF) of 5670 and 5684 is 14.

GCF(5670,5684) = 14

We will now calculate the prime factors of 5670 and 5684, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 5670 and 5684.

How to find the GCF of 5670 and 5684?

We will first find the prime factorization of 5670 and 5684. After we will calculate the factors of 5670 and 5684 and find the biggest common factor number .

Step-1: Prime Factorization of 5670

Prime factors of 5670 are 2, 3, 5, 7. Prime factorization of 5670 in exponential form is:

5670 = 2¹ × 3⁴ × 5¹ × 7¹

Step-2: Prime Factorization of 5684

Prime factors of 5684 are 2, 7, 29. Prime factorization of 5684 in exponential form is:

5684 = 2² × 7² × 29¹

Step-3: Factors of 5670

List of positive integer factors of 5670 that divides 5670 without a remainder.

1, 2, 3, 5, 6, 7, 9, 10, 14, 15, 18, 21, 27, 30, 35, 42, 45, 54, 63, 70, 81, 90, 105, 126, 135, 162, 189, 210, 270, 315, 378, 405, 567, 630, 810, 945, 1134, 1890, 2835

Step-4: Factors of 5684

List of positive integer factors of 5684 that divides 5670 without a remainder.

1, 2, 4, 7, 14, 28, 29, 49, 58, 98, 116, 196, 203, 406, 812, 1421, 2842

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 5670 and 5684. The biggest common factor number is the GCF number.
So the greatest common factor 5670 and 5684 is 14.

Also check out the Least Common Multiple of 5670 and 5684