What is the Greatest Common Factor of 4200 and 4220?

Greatest common factor (GCF) of 4200 and 4220 is 20.

GCF(4200,4220) = 20

We will now calculate the prime factors of 4200 and 4220, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 4200 and 4220.

How to find the GCF of 4200 and 4220?

We will first find the prime factorization of 4200 and 4220. After we will calculate the factors of 4200 and 4220 and find the biggest common factor number .

Step-1: Prime Factorization of 4200

Prime factors of 4200 are 2, 3, 5, 7. Prime factorization of 4200 in exponential form is:

4200 = 2³ × 3¹ × 5² × 7¹

Step-2: Prime Factorization of 4220

Prime factors of 4220 are 2, 5, 211. Prime factorization of 4220 in exponential form is:

4220 = 2² × 5¹ × 211¹

Step-3: Factors of 4200

List of positive integer factors of 4200 that divides 4200 without a remainder.

1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24, 25, 28, 30, 35, 40, 42, 50, 56, 60, 70, 75, 84, 100, 105, 120, 140, 150, 168, 175, 200, 210, 280, 300, 350, 420, 525, 600, 700, 840, 1050, 1400, 2100

Step-4: Factors of 4220

List of positive integer factors of 4220 that divides 4200 without a remainder.

1, 2, 4, 5, 10, 20, 211, 422, 844, 1055, 2110

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 4200 and 4220. The biggest common factor number is the GCF number.
So the greatest common factor 4200 and 4220 is 20.

Also check out the Least Common Multiple of 4200 and 4220