What is the Greatest Common Factor of 420 and 432?

Greatest common factor (GCF) of 420 and 432 is 12.

GCF(420,432) = 12

We will now calculate the prime factors of 420 and 432, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 420 and 432.

How to find the GCF of 420 and 432?

We will first find the prime factorization of 420 and 432. After we will calculate the factors of 420 and 432 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 432

Prime factors of 432 are 2, 3. Prime factorization of 432 in exponential form is:

432 = 2⁴ × 3³

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 432

List of positive integer factors of 432 that divides 420 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 36, 48, 54, 72, 108, 144, 216

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 420 and 432. The biggest common factor number is the GCF number.
So the greatest common factor 420 and 432 is 12.

Also check out the Least Common Multiple of 420 and 432