What is the Greatest Common Factor of 4190 and 4200?

Greatest common factor (GCF) of 4190 and 4200 is 10.

GCF(4190,4200) = 10

We will now calculate the prime factors of 4190 and 4200, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 4190 and 4200.

How to find the GCF of 4190 and 4200?

We will first find the prime factorization of 4190 and 4200. After we will calculate the factors of 4190 and 4200 and find the biggest common factor number .

Step-1: Prime Factorization of 4190

Prime factors of 4190 are 2, 5, 419. Prime factorization of 4190 in exponential form is:

4190 = 2¹ × 5¹ × 419¹

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 4190

List of positive integer factors of 4190 that divides 4190 without a remainder.

1, 2, 5, 10, 419, 838, 2095

Step-4: Factors of 4200

List of positive integer factors of 4200 that divides 4190 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 4190 and 4200. The biggest common factor number is the GCF number.
So the greatest common factor 4190 and 4200 is 10.

Also check out the Least Common Multiple of 4190 and 4200