What is the Greatest Common Factor of 409 and 428?

Greatest common factor (GCF) of 409 and 428 is 1.

GCF(409,428) = 1

We will now calculate the prime factors of 409 and 428, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 409 and 428.

How to find the GCF of 409 and 428?

We will first find the prime factorization of 409 and 428. After we will calculate the factors of 409 and 428 and find the biggest common factor number .

Step-1: Prime Factorization of 409

Prime factors of 409 are 409. Prime factorization of 409 in exponential form is:

409 = 409¹

Step-2: Prime Factorization of 428

Prime factors of 428 are 2, 107. Prime factorization of 428 in exponential form is:

428 = 2² × 107¹

Step-3: Factors of 409

List of positive integer factors of 409 that divides 409 without a remainder.

Step-4: Factors of 428

List of positive integer factors of 428 that divides 409 without a remainder.

1, 2, 4, 107, 214

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 409 and 428. The biggest common factor number is the GCF number.
So the greatest common factor 409 and 428 is 1.

Also check out the Least Common Multiple of 409 and 428