What is the Greatest Common Factor of 78174 and 78189?

Greatest common factor (GCF) of 78174 and 78189 is 3.

GCF(78174,78189) = 3

We will now calculate the prime factors of 78174 and 78189, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 78174 and 78189.

How to find the GCF of 78174 and 78189?

We will first find the prime factorization of 78174 and 78189. After we will calculate the factors of 78174 and 78189 and find the biggest common factor number .

Step-1: Prime Factorization of 78174

Prime factors of 78174 are 2, 3, 43, 101. Prime factorization of 78174 in exponential form is:

78174 = 2¹ × 3² × 43¹ × 101¹

Step-2: Prime Factorization of 78189

Prime factors of 78189 are 3, 67, 389. Prime factorization of 78189 in exponential form is:

78189 = 3¹ × 67¹ × 389¹

Step-3: Factors of 78174

List of positive integer factors of 78174 that divides 78174 without a remainder.

1, 2, 3, 6, 9, 18, 43, 86, 101, 129, 202, 258, 303, 387, 606, 774, 909, 1818, 4343, 8686, 13029, 26058, 39087

Step-4: Factors of 78189

List of positive integer factors of 78189 that divides 78174 without a remainder.

1, 3, 67, 201, 389, 1167, 26063

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 78174 and 78189. The biggest common factor number is the GCF number.
So the greatest common factor 78174 and 78189 is 3.

Also check out the Least Common Multiple of 78174 and 78189