What is the Greatest Common Factor of 4200 and 4214?

Greatest common factor (GCF) of 4200 and 4214 is 14.

GCF(4200,4214) = 14

We will now calculate the prime factors of 4200 and 4214, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 4200 and 4214.

How to find the GCF of 4200 and 4214?

We will first find the prime factorization of 4200 and 4214. After we will calculate the factors of 4200 and 4214 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 4214

Prime factors of 4214 are 2, 7, 43. Prime factorization of 4214 in exponential form is:

4214 = 2¹ × 7² × 43¹

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 4214

List of positive integer factors of 4214 that divides 4200 without a remainder.

1, 2, 7, 14, 43, 49, 86, 98, 301, 602, 2107

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 4200 and 4214. The biggest common factor number is the GCF number.
So the greatest common factor 4200 and 4214 is 14.

Also check out the Least Common Multiple of 4200 and 4214