What is the Greatest Common Factor of 200 and 219?

Greatest common factor (GCF) of 200 and 219 is 1.

GCF(200,219) = 1

We will now calculate the prime factors of 200 and 219, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 200 and 219.

How to find the GCF of 200 and 219?

We will first find the prime factorization of 200 and 219. After we will calculate the factors of 200 and 219 and find the biggest common factor number .

Step-1: Prime Factorization of 200

Prime factors of 200 are 2, 5. Prime factorization of 200 in exponential form is:

200 = 2³ × 5²

Step-2: Prime Factorization of 219

Prime factors of 219 are 3, 73. Prime factorization of 219 in exponential form is:

219 = 3¹ × 73¹

Step-3: Factors of 200

List of positive integer factors of 200 that divides 200 without a remainder.

1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100

Step-4: Factors of 219

List of positive integer factors of 219 that divides 200 without a remainder.

1, 3, 73

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 200 and 219. The biggest common factor number is the GCF number.
So the greatest common factor 200 and 219 is 1.

Also check out the Least Common Multiple of 200 and 219