What is the Greatest Common Factor of 4200 and 4212?

Greatest common factor (GCF) of 4200 and 4212 is 12.

GCF(4200,4212) = 12

We will now calculate the prime factors of 4200 and 4212, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 4200 and 4212.

How to find the GCF of 4200 and 4212?

We will first find the prime factorization of 4200 and 4212. After we will calculate the factors of 4200 and 4212 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 4212

Prime factors of 4212 are 2, 3, 13. Prime factorization of 4212 in exponential form is:

4212 = 2² × 3⁴ × 13¹

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 4212

List of positive integer factors of 4212 that divides 4200 without a remainder.

1, 2, 3, 4, 6, 9, 12, 13, 18, 26, 27, 36, 39, 52, 54, 78, 81, 108, 117, 156, 162, 234, 324, 351, 468, 702, 1053, 1404, 2106

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 4200 and 4212. The biggest common factor number is the GCF number.
So the greatest common factor 4200 and 4212 is 12.

Also check out the Least Common Multiple of 4200 and 4212