What is the Greatest Common Factor of 414 and 426?

Greatest common factor (GCF) of 414 and 426 is 6.

GCF(414,426) = 6

We will now calculate the prime factors of 414 and 426, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 414 and 426.

How to find the GCF of 414 and 426?

We will first find the prime factorization of 414 and 426. After we will calculate the factors of 414 and 426 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 426

Prime factors of 426 are 2, 3, 71. Prime factorization of 426 in exponential form is:

426 = 2¹ × 3¹ × 71¹

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 426

List of positive integer factors of 426 that divides 414 without a remainder.

1, 2, 3, 6, 71, 142, 213

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 414 and 426. The biggest common factor number is the GCF number.
So the greatest common factor 414 and 426 is 6.

Also check out the Least Common Multiple of 414 and 426