What is the Greatest Common Factor of 392 and 406?

Greatest common factor (GCF) of 392 and 406 is 14.

GCF(392,406) = 14

We will now calculate the prime factors of 392 and 406, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 392 and 406.

How to find the GCF of 392 and 406?

We will first find the prime factorization of 392 and 406. After we will calculate the factors of 392 and 406 and find the biggest common factor number .

Step-1: Prime Factorization of 392

Prime factors of 392 are 2, 7. Prime factorization of 392 in exponential form is:

392 = 2³ × 7²

Step-2: 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-3: Factors of 392

List of positive integer factors of 392 that divides 392 without a remainder.

1, 2, 4, 7, 8, 14, 28, 49, 56, 98, 196

Step-4: Factors of 406

List of positive integer factors of 406 that divides 392 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 392 and 406. The biggest common factor number is the GCF number.
So the greatest common factor 392 and 406 is 14.

Also check out the Least Common Multiple of 392 and 406