What is the Greatest Common Factor of 420 and 434?

Greatest common factor (GCF) of 420 and 434 is 14.

GCF(420,434) = 14

We will now calculate the prime factors of 420 and 434, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 420 and 434.

How to find the GCF of 420 and 434?

We will first find the prime factorization of 420 and 434. After we will calculate the factors of 420 and 434 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 434

Prime factors of 434 are 2, 7, 31. Prime factorization of 434 in exponential form is:

434 = 2¹ × 7¹ × 31¹

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 434

List of positive integer factors of 434 that divides 420 without a remainder.

1, 2, 7, 14, 31, 62, 217

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 420 and 434. The biggest common factor number is the GCF number.
So the greatest common factor 420 and 434 is 14.

Also check out the Least Common Multiple of 420 and 434