What is the Greatest Common Factor of 7214 and 7225?

Greatest common factor (GCF) of 7214 and 7225 is 1.

GCF(7214,7225) = 1

We will now calculate the prime factors of 7214 and 7225, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 7214 and 7225.

How to find the GCF of 7214 and 7225?

We will first find the prime factorization of 7214 and 7225. After we will calculate the factors of 7214 and 7225 and find the biggest common factor number .

Step-1: Prime Factorization of 7214

Prime factors of 7214 are 2, 3607. Prime factorization of 7214 in exponential form is:

7214 = 2¹ × 3607¹

Step-2: Prime Factorization of 7225

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

7225 = 5² × 17²

Step-3: Factors of 7214

List of positive integer factors of 7214 that divides 7214 without a remainder.

1, 2, 3607

Step-4: Factors of 7225

List of positive integer factors of 7225 that divides 7214 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 7214 and 7225. The biggest common factor number is the GCF number.
So the greatest common factor 7214 and 7225 is 1.

Also check out the Least Common Multiple of 7214 and 7225