What is the Greatest Common Factor of 5600 and 5614?

Greatest common factor (GCF) of 5600 and 5614 is 14.

GCF(5600,5614) = 14

We will now calculate the prime factors of 5600 and 5614, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 5600 and 5614.

How to find the GCF of 5600 and 5614?

We will first find the prime factorization of 5600 and 5614. After we will calculate the factors of 5600 and 5614 and find the biggest common factor number .

Step-1: Prime Factorization of 5600

Prime factors of 5600 are 2, 5, 7. Prime factorization of 5600 in exponential form is:

5600 = 2⁵ × 5² × 7¹

Step-2: Prime Factorization of 5614

Prime factors of 5614 are 2, 7, 401. Prime factorization of 5614 in exponential form is:

5614 = 2¹ × 7¹ × 401¹

Step-3: Factors of 5600

List of positive integer factors of 5600 that divides 5600 without a remainder.

1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 25, 28, 32, 35, 40, 50, 56, 70, 80, 100, 112, 140, 160, 175, 200, 224, 280, 350, 400, 560, 700, 800, 1120, 1400, 2800

Step-4: Factors of 5614

List of positive integer factors of 5614 that divides 5600 without a remainder.

1, 2, 7, 14, 401, 802, 2807

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 5600 and 5614. The biggest common factor number is the GCF number.
So the greatest common factor 5600 and 5614 is 14.

Also check out the Least Common Multiple of 5600 and 5614