What is the Greatest Common Factor of 414 and 434?

Greatest common factor (GCF) of 414 and 434 is 2.

GCF(414,434) = 2

We will now calculate the prime factors of 414 and 434, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 414 and 434.

How to find the GCF of 414 and 434?

We will first find the prime factorization of 414 and 434. After we will calculate the factors of 414 and 434 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 434

Prime factors of 434 are 2, 7, 31. Prime factorization of 434 in exponential form is:

434 = 2¹ × 7¹ × 31¹

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 434

List of positive integer factors of 434 that divides 414 without a remainder.

1, 2, 7, 14, 31, 62, 217

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 414 and 434. The biggest common factor number is the GCF number.
So the greatest common factor 414 and 434 is 2.

Also check out the Least Common Multiple of 414 and 434