What is the Greatest Common Factor of 414 and 420?

Greatest common factor (GCF) of 414 and 420 is 6.

GCF(414,420) = 6

We will now calculate the prime factors of 414 and 420, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 414 and 420.

How to find the GCF of 414 and 420?

We will first find the prime factorization of 414 and 420. After we will calculate the factors of 414 and 420 and find the biggest common factor number .

Step-1: Prime Factorization of 414

Prime factors of 414 are 2, 3, 23. Prime factorization of 414 in exponential form is:

414 = 2¹ × 3² × 23¹

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 414

List of positive integer factors of 414 that divides 414 without a remainder.

1, 2, 3, 6, 9, 18, 23, 46, 69, 138, 207

Step-4: Factors of 420

List of positive integer factors of 420 that divides 414 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 414 and 420. The biggest common factor number is the GCF number.
So the greatest common factor 414 and 420 is 6.

Also check out the Least Common Multiple of 414 and 420