What is the Greatest Common Factor of 32094 and 32109?

Greatest common factor (GCF) of 32094 and 32109 is 3.

GCF(32094,32109) = 3

We will now calculate the prime factors of 32094 and 32109, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 32094 and 32109.

How to find the GCF of 32094 and 32109?

We will first find the prime factorization of 32094 and 32109. After we will calculate the factors of 32094 and 32109 and find the biggest common factor number .

Step-1: Prime Factorization of 32094

Prime factors of 32094 are 2, 3, 1783. Prime factorization of 32094 in exponential form is:

32094 = 2¹ × 3² × 1783¹

Step-2: Prime Factorization of 32109

Prime factors of 32109 are 3, 7, 11, 139. Prime factorization of 32109 in exponential form is:

32109 = 3¹ × 7¹ × 11¹ × 139¹

Step-3: Factors of 32094

List of positive integer factors of 32094 that divides 32094 without a remainder.

1, 2, 3, 6, 9, 18, 1783, 3566, 5349, 10698, 16047

Step-4: Factors of 32109

List of positive integer factors of 32109 that divides 32094 without a remainder.

1, 3, 7, 11, 21, 33, 77, 139, 231, 417, 973, 1529, 2919, 4587, 10703

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 32094 and 32109. The biggest common factor number is the GCF number.
So the greatest common factor 32094 and 32109 is 3.

Also check out the Least Common Multiple of 32094 and 32109