What is the Greatest Common Factor of 403 and 408?

Greatest common factor (GCF) of 403 and 408 is 1.

GCF(403,408) = 1

We will now calculate the prime factors of 403 and 408, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 403 and 408.

How to find the GCF of 403 and 408?

We will first find the prime factorization of 403 and 408. After we will calculate the factors of 403 and 408 and find the biggest common factor number .

Step-1: Prime Factorization of 403

Prime factors of 403 are 13, 31. Prime factorization of 403 in exponential form is:

403 = 13¹ × 31¹

Step-2: Prime Factorization of 408

Prime factors of 408 are 2, 3, 17. Prime factorization of 408 in exponential form is:

408 = 2³ × 3¹ × 17¹

Step-3: Factors of 403

List of positive integer factors of 403 that divides 403 without a remainder.

1, 13, 31

Step-4: Factors of 408

List of positive integer factors of 408 that divides 403 without a remainder.

1, 2, 3, 4, 6, 8, 12, 17, 24, 34, 51, 68, 102, 136, 204

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 403 and 408. The biggest common factor number is the GCF number.
So the greatest common factor 403 and 408 is 1.

Also check out the Least Common Multiple of 403 and 408