What is the Greatest Common Factor of 10408 and 10414?

Greatest common factor (GCF) of 10408 and 10414 is 2.

GCF(10408,10414) = 2

We will now calculate the prime factors of 10408 and 10414, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10408 and 10414.

How to find the GCF of 10408 and 10414?

We will first find the prime factorization of 10408 and 10414. After we will calculate the factors of 10408 and 10414 and find the biggest common factor number .

Step-1: Prime Factorization of 10408

Prime factors of 10408 are 2, 1301. Prime factorization of 10408 in exponential form is:

10408 = 2³ × 1301¹

Step-2: Prime Factorization of 10414

Prime factors of 10414 are 2, 41, 127. Prime factorization of 10414 in exponential form is:

10414 = 2¹ × 41¹ × 127¹

Step-3: Factors of 10408

List of positive integer factors of 10408 that divides 10408 without a remainder.

1, 2, 4, 8, 1301, 2602, 5204

Step-4: Factors of 10414

List of positive integer factors of 10414 that divides 10408 without a remainder.

1, 2, 41, 82, 127, 254, 5207

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 10408 and 10414. The biggest common factor number is the GCF number.
So the greatest common factor 10408 and 10414 is 2.

Also check out the Least Common Multiple of 10408 and 10414