What is the Greatest Common Factor of 414 and 424?

Greatest common factor (GCF) of 414 and 424 is 2.

GCF(414,424) = 2

We will now calculate the prime factors of 414 and 424, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 414 and 424.

How to find the GCF of 414 and 424?

We will first find the prime factorization of 414 and 424. After we will calculate the factors of 414 and 424 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 424

Prime factors of 424 are 2, 53. Prime factorization of 424 in exponential form is:

424 = 2³ × 53¹

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 424

List of positive integer factors of 424 that divides 414 without a remainder.

1, 2, 4, 8, 53, 106, 212

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 414 and 424. The biggest common factor number is the GCF number.
So the greatest common factor 414 and 424 is 2.

Also check out the Least Common Multiple of 414 and 424