What is the Greatest Common Factor of 408 and 420?

Greatest common factor (GCF) of 408 and 420 is 12.

GCF(408,420) = 12

We will now calculate the prime factors of 408 and 420, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 408 and 420.

How to find the GCF of 408 and 420?

We will first find the prime factorization of 408 and 420. After we will calculate the factors of 408 and 420 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 420

Prime factors of 420 are 2, 3, 5, 7. Prime factorization of 420 in exponential form is:

420 = 2² × 3¹ × 5¹ × 7¹

Step-3: Factors of 408

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

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

Step-4: Factors of 420

List of positive integer factors of 420 that divides 408 without a remainder.

1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 408 and 420. The biggest common factor number is the GCF number.
So the greatest common factor 408 and 420 is 12.

Also check out the Least Common Multiple of 408 and 420