What is the Greatest Common Factor of 5230 and 5250?

Greatest common factor (GCF) of 5230 and 5250 is 10.

GCF(5230,5250) = 10

We will now calculate the prime factors of 5230 and 5250, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 5230 and 5250.

How to find the GCF of 5230 and 5250?

We will first find the prime factorization of 5230 and 5250. After we will calculate the factors of 5230 and 5250 and find the biggest common factor number .

Step-1: Prime Factorization of 5230

Prime factors of 5230 are 2, 5, 523. Prime factorization of 5230 in exponential form is:

5230 = 2¹ × 5¹ × 523¹

Step-2: Prime Factorization of 5250

Prime factors of 5250 are 2, 3, 5, 7. Prime factorization of 5250 in exponential form is:

5250 = 2¹ × 3¹ × 5³ × 7¹

Step-3: Factors of 5230

List of positive integer factors of 5230 that divides 5230 without a remainder.

1, 2, 5, 10, 523, 1046, 2615

Step-4: Factors of 5250

List of positive integer factors of 5250 that divides 5230 without a remainder.

1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 25, 30, 35, 42, 50, 70, 75, 105, 125, 150, 175, 210, 250, 350, 375, 525, 750, 875, 1050, 1750, 2625

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 5230 and 5250. The biggest common factor number is the GCF number.
So the greatest common factor 5230 and 5250 is 10.

Also check out the Least Common Multiple of 5230 and 5250