What is the Greatest Common Factor of 4185 and 4200?

Greatest common factor (GCF) of 4185 and 4200 is 15.

GCF(4185,4200) = 15

We will now calculate the prime factors of 4185 and 4200, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 4185 and 4200.

How to find the GCF of 4185 and 4200?

We will first find the prime factorization of 4185 and 4200. After we will calculate the factors of 4185 and 4200 and find the biggest common factor number .

Step-1: Prime Factorization of 4185

Prime factors of 4185 are 3, 5, 31. Prime factorization of 4185 in exponential form is:

4185 = 3³ × 5¹ × 31¹

Step-2: 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-3: Factors of 4185

List of positive integer factors of 4185 that divides 4185 without a remainder.

1, 3, 5, 9, 15, 27, 31, 45, 93, 135, 155, 279, 465, 837, 1395

Step-4: Factors of 4200

List of positive integer factors of 4200 that divides 4185 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 4185 and 4200. The biggest common factor number is the GCF number.
So the greatest common factor 4185 and 4200 is 15.

Also check out the Least Common Multiple of 4185 and 4200