What is the Greatest Common Factor of 414 and 425?

Greatest common factor (GCF) of 414 and 425 is 1.

GCF(414,425) = 1

We will now calculate the prime factors of 414 and 425, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 414 and 425.

How to find the GCF of 414 and 425?

We will first find the prime factorization of 414 and 425. After we will calculate the factors of 414 and 425 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 425

Prime factors of 425 are 5, 17. Prime factorization of 425 in exponential form is:

425 = 5² × 17¹

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 425

List of positive integer factors of 425 that divides 414 without a remainder.

1, 5, 17, 25, 85

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 414 and 425. The biggest common factor number is the GCF number.
So the greatest common factor 414 and 425 is 1.

Also check out the Least Common Multiple of 414 and 425