What is the Greatest Common Factor of 10414 and 10422?

Greatest common factor (GCF) of 10414 and 10422 is 2.

GCF(10414,10422) = 2

We will now calculate the prime factors of 10414 and 10422, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10414 and 10422.

How to find the GCF of 10414 and 10422?

We will first find the prime factorization of 10414 and 10422. After we will calculate the factors of 10414 and 10422 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 10422

Prime factors of 10422 are 2, 3, 193. Prime factorization of 10422 in exponential form is:

10422 = 2¹ × 3³ × 193¹

Step-3: Factors of 10414

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

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

Step-4: Factors of 10422

List of positive integer factors of 10422 that divides 10414 without a remainder.

1, 2, 3, 6, 9, 18, 27, 54, 193, 386, 579, 1158, 1737, 3474, 5211

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 10414 and 10422. The biggest common factor number is the GCF number.
So the greatest common factor 10414 and 10422 is 2.

Also check out the Least Common Multiple of 10414 and 10422