What is the Greatest Common Factor of 5585 and 5600?

Greatest common factor (GCF) of 5585 and 5600 is 5.

GCF(5585,5600) = 5

We will now calculate the prime factors of 5585 and 5600, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 5585 and 5600.

How to find the GCF of 5585 and 5600?

We will first find the prime factorization of 5585 and 5600. After we will calculate the factors of 5585 and 5600 and find the biggest common factor number .

Step-1: Prime Factorization of 5585

Prime factors of 5585 are 5, 1117. Prime factorization of 5585 in exponential form is:

5585 = 5¹ × 1117¹

Step-2: 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-3: Factors of 5585

List of positive integer factors of 5585 that divides 5585 without a remainder.

1, 5, 1117

Step-4: Factors of 5600

List of positive integer factors of 5600 that divides 5585 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 5585 and 5600. The biggest common factor number is the GCF number.
So the greatest common factor 5585 and 5600 is 5.

Also check out the Least Common Multiple of 5585 and 5600