What is the Greatest Common Factor of 4200 and 4208?

Greatest common factor (GCF) of 4200 and 4208 is 8.

GCF(4200,4208) = 8

We will now calculate the prime factors of 4200 and 4208, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 4200 and 4208.

How to find the GCF of 4200 and 4208?

We will first find the prime factorization of 4200 and 4208. After we will calculate the factors of 4200 and 4208 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 4208

Prime factors of 4208 are 2, 263. Prime factorization of 4208 in exponential form is:

4208 = 2⁴ × 263¹

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 4208

List of positive integer factors of 4208 that divides 4200 without a remainder.

1, 2, 4, 8, 16, 263, 526, 1052, 2104

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 4200 and 4208. The biggest common factor number is the GCF number.
So the greatest common factor 4200 and 4208 is 8.

Also check out the Least Common Multiple of 4200 and 4208