What is the Greatest Common Factor of 410 and 414?

Greatest common factor (GCF) of 410 and 414 is 2.

GCF(410,414) = 2

We will now calculate the prime factors of 410 and 414, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 410 and 414.

How to find the GCF of 410 and 414?

We will first find the prime factorization of 410 and 414. After we will calculate the factors of 410 and 414 and find the biggest common factor number .

Step-1: Prime Factorization of 410

Prime factors of 410 are 2, 5, 41. Prime factorization of 410 in exponential form is:

410 = 2¹ × 5¹ × 41¹

Step-2: 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-3: Factors of 410

List of positive integer factors of 410 that divides 410 without a remainder.

1, 2, 5, 10, 41, 82, 205

Step-4: Factors of 414

List of positive integer factors of 414 that divides 410 without a remainder.

1, 2, 3, 6, 9, 18, 23, 46, 69, 138, 207

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 410 and 414. The biggest common factor number is the GCF number.
So the greatest common factor 410 and 414 is 2.

Also check out the Least Common Multiple of 410 and 414