What is the Greatest Common Factor of 420 and 427?

Greatest common factor (GCF) of 420 and 427 is 7.

GCF(420,427) = 7

We will now calculate the prime factors of 420 and 427, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 420 and 427.

How to find the GCF of 420 and 427?

We will first find the prime factorization of 420 and 427. After we will calculate the factors of 420 and 427 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 427

Prime factors of 427 are 7, 61. Prime factorization of 427 in exponential form is:

427 = 7¹ × 61¹

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 427

List of positive integer factors of 427 that divides 420 without a remainder.

1, 7, 61

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 420 and 427. The biggest common factor number is the GCF number.
So the greatest common factor 420 and 427 is 7.

Also check out the Least Common Multiple of 420 and 427