What is the Greatest Common Factor of 5200 and 5215?

Greatest common factor (GCF) of 5200 and 5215 is 5.

GCF(5200,5215) = 5

We will now calculate the prime factors of 5200 and 5215, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 5200 and 5215.

How to find the GCF of 5200 and 5215?

We will first find the prime factorization of 5200 and 5215. After we will calculate the factors of 5200 and 5215 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 5215

Prime factors of 5215 are 5, 7, 149. Prime factorization of 5215 in exponential form is:

5215 = 5¹ × 7¹ × 149¹

Step-3: Factors of 5200

List of positive integer factors of 5200 that divides 5200 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

Step-4: Factors of 5215

List of positive integer factors of 5215 that divides 5200 without a remainder.

1, 5, 7, 35, 149, 745, 1043

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 5200 and 5215. The biggest common factor number is the GCF number.
So the greatest common factor 5200 and 5215 is 5.

Also check out the Least Common Multiple of 5200 and 5215