What is the Greatest Common Factor of 4186 and 4200?

Greatest common factor (GCF) of 4186 and 4200 is 14.

GCF(4186,4200) = 14

We will now calculate the prime factors of 4186 and 4200, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 4186 and 4200.

How to find the GCF of 4186 and 4200?

We will first find the prime factorization of 4186 and 4200. After we will calculate the factors of 4186 and 4200 and find the biggest common factor number .

Step-1: Prime Factorization of 4186

Prime factors of 4186 are 2, 7, 13, 23. Prime factorization of 4186 in exponential form is:

4186 = 2¹ × 7¹ × 13¹ × 23¹

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 4186

List of positive integer factors of 4186 that divides 4186 without a remainder.

1, 2, 7, 13, 14, 23, 26, 46, 91, 161, 182, 299, 322, 598, 2093

Step-4: Factors of 4200

List of positive integer factors of 4200 that divides 4186 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 4186 and 4200. The biggest common factor number is the GCF number.
So the greatest common factor 4186 and 4200 is 14.

Also check out the Least Common Multiple of 4186 and 4200