What is the Greatest Common Factor of 7290 and 7310?

Greatest common factor (GCF) of 7290 and 7310 is 10.

GCF(7290,7310) = 10

We will now calculate the prime factors of 7290 and 7310, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 7290 and 7310.

How to find the GCF of 7290 and 7310?

We will first find the prime factorization of 7290 and 7310. After we will calculate the factors of 7290 and 7310 and find the biggest common factor number .

Step-1: Prime Factorization of 7290

Prime factors of 7290 are 2, 3, 5. Prime factorization of 7290 in exponential form is:

7290 = 2¹ × 3⁶ × 5¹

Step-2: Prime Factorization of 7310

Prime factors of 7310 are 2, 5, 17, 43. Prime factorization of 7310 in exponential form is:

7310 = 2¹ × 5¹ × 17¹ × 43¹

Step-3: Factors of 7290

List of positive integer factors of 7290 that divides 7290 without a remainder.

1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 81, 90, 135, 162, 243, 270, 405, 486, 729, 810, 1215, 1458, 2430, 3645

Step-4: Factors of 7310

List of positive integer factors of 7310 that divides 7290 without a remainder.

1, 2, 5, 10, 17, 34, 43, 85, 86, 170, 215, 430, 731, 1462, 3655

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 7290 and 7310. The biggest common factor number is the GCF number.
So the greatest common factor 7290 and 7310 is 10.

Also check out the Least Common Multiple of 7290 and 7310