What is the Greatest Common Factor of 414 and 423?

Greatest common factor (GCF) of 414 and 423 is 9.

GCF(414,423) = 9

We will now calculate the prime factors of 414 and 423, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 414 and 423.

How to find the GCF of 414 and 423?

We will first find the prime factorization of 414 and 423. After we will calculate the factors of 414 and 423 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 423

Prime factors of 423 are 3, 47. Prime factorization of 423 in exponential form is:

423 = 3² × 47¹

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 423

List of positive integer factors of 423 that divides 414 without a remainder.

1, 3, 9, 47, 141

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 414 and 423. The biggest common factor number is the GCF number.
So the greatest common factor 414 and 423 is 9.

Also check out the Least Common Multiple of 414 and 423