What is the Greatest Common Factor of 7225 and 7240?

Greatest common factor (GCF) of 7225 and 7240 is 5.

GCF(7225,7240) = 5

We will now calculate the prime factors of 7225 and 7240, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 7225 and 7240.

How to find the GCF of 7225 and 7240?

We will first find the prime factorization of 7225 and 7240. After we will calculate the factors of 7225 and 7240 and find the biggest common factor number .

Step-1: Prime Factorization of 7225

Prime factors of 7225 are 5, 17. Prime factorization of 7225 in exponential form is:

7225 = 5² × 17²

Step-2: Prime Factorization of 7240

Prime factors of 7240 are 2, 5, 181. Prime factorization of 7240 in exponential form is:

7240 = 2³ × 5¹ × 181¹

Step-3: Factors of 7225

List of positive integer factors of 7225 that divides 7225 without a remainder.

1, 5, 17, 25, 85, 289, 425, 1445

Step-4: Factors of 7240

List of positive integer factors of 7240 that divides 7225 without a remainder.

1, 2, 4, 5, 8, 10, 20, 40, 181, 362, 724, 905, 1448, 1810, 3620

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 7225 and 7240. The biggest common factor number is the GCF number.
So the greatest common factor 7225 and 7240 is 5.

Also check out the Least Common Multiple of 7225 and 7240