What is the Greatest Common Factor of 189 and 203?

Greatest common factor (GCF) of 189 and 203 is 7.

GCF(189,203) = 7

We will now calculate the prime factors of 189 and 203, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 189 and 203.

How to find the GCF of 189 and 203?

We will first find the prime factorization of 189 and 203. After we will calculate the factors of 189 and 203 and find the biggest common factor number .

Step-1: Prime Factorization of 189

Prime factors of 189 are 3, 7. Prime factorization of 189 in exponential form is:

189 = 3³ × 7¹

Step-2: Prime Factorization of 203

Prime factors of 203 are 7, 29. Prime factorization of 203 in exponential form is:

203 = 7¹ × 29¹

Step-3: Factors of 189

List of positive integer factors of 189 that divides 189 without a remainder.

1, 3, 7, 9, 21, 27, 63

Step-4: Factors of 203

List of positive integer factors of 203 that divides 189 without a remainder.

1, 7, 29

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 189 and 203. The biggest common factor number is the GCF number.
So the greatest common factor 189 and 203 is 7.

Also check out the Least Common Multiple of 189 and 203