What is the Greatest Common Factor of 7409 and 7414?

Greatest common factor (GCF) of 7409 and 7414 is 1.

GCF(7409,7414) = 1

We will now calculate the prime factors of 7409 and 7414, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 7409 and 7414.

How to find the GCF of 7409 and 7414?

We will first find the prime factorization of 7409 and 7414. After we will calculate the factors of 7409 and 7414 and find the biggest common factor number .

Step-1: Prime Factorization of 7409

Prime factors of 7409 are 31, 239. Prime factorization of 7409 in exponential form is:

7409 = 31¹ × 239¹

Step-2: Prime Factorization of 7414

Prime factors of 7414 are 2, 11, 337. Prime factorization of 7414 in exponential form is:

7414 = 2¹ × 11¹ × 337¹

Step-3: Factors of 7409

List of positive integer factors of 7409 that divides 7409 without a remainder.

1, 31, 239

Step-4: Factors of 7414

List of positive integer factors of 7414 that divides 7409 without a remainder.

1, 2, 11, 22, 337, 674, 3707

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 7409 and 7414. The biggest common factor number is the GCF number.
So the greatest common factor 7409 and 7414 is 1.

Also check out the Least Common Multiple of 7409 and 7414