What is the Greatest Common Factor of 414 and 422?

Greatest common factor (GCF) of 414 and 422 is 2.

GCF(414,422) = 2

We will now calculate the prime factors of 414 and 422, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 414 and 422.

How to find the GCF of 414 and 422?

We will first find the prime factorization of 414 and 422. After we will calculate the factors of 414 and 422 and find the biggest common factor number .

Step-1: Prime Factorization of 414

Prime factors of 414 are 2, 3, 23. Prime factorization of 414 in exponential form is:

414 = 2¹ × 3² × 23¹

Step-2: Prime Factorization of 422

Prime factors of 422 are 2, 211. Prime factorization of 422 in exponential form is:

422 = 2¹ × 211¹

Step-3: Factors of 414

List of positive integer factors of 414 that divides 414 without a remainder.

1, 2, 3, 6, 9, 18, 23, 46, 69, 138, 207

Step-4: Factors of 422

List of positive integer factors of 422 that divides 414 without a remainder.

1, 2, 211

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 414 and 422. The biggest common factor number is the GCF number.
So the greatest common factor 414 and 422 is 2.

Also check out the Least Common Multiple of 414 and 422