What is the Greatest Common Factor of 420 and 438?

Greatest common factor (GCF) of 420 and 438 is 6.

GCF(420,438) = 6

We will now calculate the prime factors of 420 and 438, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 420 and 438.

How to find the GCF of 420 and 438?

We will first find the prime factorization of 420 and 438. After we will calculate the factors of 420 and 438 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 438

Prime factors of 438 are 2, 3, 73. Prime factorization of 438 in exponential form is:

438 = 2¹ × 3¹ × 73¹

Step-3: Factors of 420

List of positive integer factors of 420 that divides 420 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

Step-4: Factors of 438

List of positive integer factors of 438 that divides 420 without a remainder.

1, 2, 3, 6, 73, 146, 219

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 420 and 438. The biggest common factor number is the GCF number.
So the greatest common factor 420 and 438 is 6.

Also check out the Least Common Multiple of 420 and 438