What is the Greatest Common Factor of 5680 and 5700?

Greatest common factor (GCF) of 5680 and 5700 is 20.

GCF(5680,5700) = 20

We will now calculate the prime factors of 5680 and 5700, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 5680 and 5700.

How to find the GCF of 5680 and 5700?

We will first find the prime factorization of 5680 and 5700. After we will calculate the factors of 5680 and 5700 and find the biggest common factor number .

Step-1: Prime Factorization of 5680

Prime factors of 5680 are 2, 5, 71. Prime factorization of 5680 in exponential form is:

5680 = 2⁴ × 5¹ × 71¹

Step-2: Prime Factorization of 5700

Prime factors of 5700 are 2, 3, 5, 19. Prime factorization of 5700 in exponential form is:

5700 = 2² × 3¹ × 5² × 19¹

Step-3: Factors of 5680

List of positive integer factors of 5680 that divides 5680 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 40, 71, 80, 142, 284, 355, 568, 710, 1136, 1420, 2840

Step-4: Factors of 5700

List of positive integer factors of 5700 that divides 5680 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 15, 19, 20, 25, 30, 38, 50, 57, 60, 75, 76, 95, 100, 114, 150, 190, 228, 285, 300, 380, 475, 570, 950, 1140, 1425, 1900, 2850

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 5680 and 5700. The biggest common factor number is the GCF number.
So the greatest common factor 5680 and 5700 is 20.

Also check out the Least Common Multiple of 5680 and 5700