What is the Greatest Common Factor of 9200 and 9219?

Greatest common factor (GCF) of 9200 and 9219 is 1.

GCF(9200,9219) = 1

We will now calculate the prime factors of 9200 and 9219, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 9200 and 9219.

How to find the GCF of 9200 and 9219?

We will first find the prime factorization of 9200 and 9219. After we will calculate the factors of 9200 and 9219 and find the biggest common factor number .

Step-1: Prime Factorization of 9200

Prime factors of 9200 are 2, 5, 23. Prime factorization of 9200 in exponential form is:

9200 = 2⁴ × 5² × 23¹

Step-2: Prime Factorization of 9219

Prime factors of 9219 are 3, 7, 439. Prime factorization of 9219 in exponential form is:

9219 = 3¹ × 7¹ × 439¹

Step-3: Factors of 9200

List of positive integer factors of 9200 that divides 9200 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 23, 25, 40, 46, 50, 80, 92, 100, 115, 184, 200, 230, 368, 400, 460, 575, 920, 1150, 1840, 2300, 4600

Step-4: Factors of 9219

List of positive integer factors of 9219 that divides 9200 without a remainder.

1, 3, 7, 21, 439, 1317, 3073

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 9200 and 9219. The biggest common factor number is the GCF number.
So the greatest common factor 9200 and 9219 is 1.

Also check out the Least Common Multiple of 9200 and 9219