What is the Greatest Common Factor of 7214 and 7232?

Greatest common factor (GCF) of 7214 and 7232 is 2.

GCF(7214,7232) = 2

We will now calculate the prime factors of 7214 and 7232, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 7214 and 7232.

How to find the GCF of 7214 and 7232?

We will first find the prime factorization of 7214 and 7232. After we will calculate the factors of 7214 and 7232 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 7232

Prime factors of 7232 are 2, 113. Prime factorization of 7232 in exponential form is:

7232 = 2⁶ × 113¹

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 7232

List of positive integer factors of 7232 that divides 7214 without a remainder.

1, 2, 4, 8, 16, 32, 64, 113, 226, 452, 904, 1808, 3616

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 7214 and 7232. The biggest common factor number is the GCF number.
So the greatest common factor 7214 and 7232 is 2.

Also check out the Least Common Multiple of 7214 and 7232