What is the Greatest Common Factor of 7230 and 7250?

Greatest common factor (GCF) of 7230 and 7250 is 10.

GCF(7230,7250) = 10

We will now calculate the prime factors of 7230 and 7250, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 7230 and 7250.

How to find the GCF of 7230 and 7250?

We will first find the prime factorization of 7230 and 7250. After we will calculate the factors of 7230 and 7250 and find the biggest common factor number .

Step-1: Prime Factorization of 7230

Prime factors of 7230 are 2, 3, 5, 241. Prime factorization of 7230 in exponential form is:

7230 = 2¹ × 3¹ × 5¹ × 241¹

Step-2: Prime Factorization of 7250

Prime factors of 7250 are 2, 5, 29. Prime factorization of 7250 in exponential form is:

7250 = 2¹ × 5³ × 29¹

Step-3: Factors of 7230

List of positive integer factors of 7230 that divides 7230 without a remainder.

1, 2, 3, 5, 6, 10, 15, 30, 241, 482, 723, 1205, 1446, 2410, 3615

Step-4: Factors of 7250

List of positive integer factors of 7250 that divides 7230 without a remainder.

1, 2, 5, 10, 25, 29, 50, 58, 125, 145, 250, 290, 725, 1450, 3625

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 7230 and 7250. The biggest common factor number is the GCF number.
So the greatest common factor 7230 and 7250 is 10.

Also check out the Least Common Multiple of 7230 and 7250