What is the Greatest Common Factor of 420 and 430?

Greatest common factor (GCF) of 420 and 430 is 10.

GCF(420,430) = 10

We will now calculate the prime factors of 420 and 430, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 420 and 430.

How to find the GCF of 420 and 430?

We will first find the prime factorization of 420 and 430. After we will calculate the factors of 420 and 430 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 430

Prime factors of 430 are 2, 5, 43. Prime factorization of 430 in exponential form is:

430 = 2¹ × 5¹ × 43¹

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 430

List of positive integer factors of 430 that divides 420 without a remainder.

1, 2, 5, 10, 43, 86, 215

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 420 and 430. The biggest common factor number is the GCF number.
So the greatest common factor 420 and 430 is 10.

Also check out the Least Common Multiple of 420 and 430