What is the Greatest Common Factor of 5600 and 5616?

Greatest common factor (GCF) of 5600 and 5616 is 16.

GCF(5600,5616) = 16

We will now calculate the prime factors of 5600 and 5616, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 5600 and 5616.

How to find the GCF of 5600 and 5616?

We will first find the prime factorization of 5600 and 5616. After we will calculate the factors of 5600 and 5616 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 5616

Prime factors of 5616 are 2, 3, 13. Prime factorization of 5616 in exponential form is:

5616 = 2⁴ × 3³ × 13¹

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 5616

List of positive integer factors of 5616 that divides 5600 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 13, 16, 18, 24, 26, 27, 36, 39, 48, 52, 54, 72, 78, 104, 108, 117, 144, 156, 208, 216, 234, 312, 351, 432, 468, 624, 702, 936, 1404, 1872, 2808

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 5600 and 5616. The biggest common factor number is the GCF number.
So the greatest common factor 5600 and 5616 is 16.

Also check out the Least Common Multiple of 5600 and 5616