What is the Greatest Common Factor of 406 and 413?

Greatest common factor (GCF) of 406 and 413 is 7.

GCF(406,413) = 7

We will now calculate the prime factors of 406 and 413, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 406 and 413.

How to find the GCF of 406 and 413?

We will first find the prime factorization of 406 and 413. After we will calculate the factors of 406 and 413 and find the biggest common factor number .

Step-1: Prime Factorization of 406

Prime factors of 406 are 2, 7, 29. Prime factorization of 406 in exponential form is:

406 = 2¹ × 7¹ × 29¹

Step-2: Prime Factorization of 413

Prime factors of 413 are 7, 59. Prime factorization of 413 in exponential form is:

413 = 7¹ × 59¹

Step-3: Factors of 406

List of positive integer factors of 406 that divides 406 without a remainder.

1, 2, 7, 14, 29, 58, 203

Step-4: Factors of 413

List of positive integer factors of 413 that divides 406 without a remainder.

1, 7, 59

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 406 and 413. The biggest common factor number is the GCF number.
So the greatest common factor 406 and 413 is 7.

Also check out the Least Common Multiple of 406 and 413