What is the Greatest Common Factor of 5189 and 5200?

Greatest common factor (GCF) of 5189 and 5200 is 1.

GCF(5189,5200) = 1

We will now calculate the prime factors of 5189 and 5200, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 5189 and 5200.

How to find the GCF of 5189 and 5200?

We will first find the prime factorization of 5189 and 5200. After we will calculate the factors of 5189 and 5200 and find the biggest common factor number .

Step-1: Prime Factorization of 5189

Prime factors of 5189 are 5189. Prime factorization of 5189 in exponential form is:

5189 = 5189¹

Step-2: Prime Factorization of 5200

Prime factors of 5200 are 2, 5, 13. Prime factorization of 5200 in exponential form is:

5200 = 2⁴ × 5² × 13¹

Step-3: Factors of 5189

List of positive integer factors of 5189 that divides 5189 without a remainder.

Step-4: Factors of 5200

List of positive integer factors of 5200 that divides 5189 without a remainder.

1, 2, 4, 5, 8, 10, 13, 16, 20, 25, 26, 40, 50, 52, 65, 80, 100, 104, 130, 200, 208, 260, 325, 400, 520, 650, 1040, 1300, 2600

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 5189 and 5200. The biggest common factor number is the GCF number.
So the greatest common factor 5189 and 5200 is 1.

Also check out the Least Common Multiple of 5189 and 5200