GCF of 18 and 27
Find the Greatest Common Factor (GCF) of 18 and 27 with a complete step-by-step solution. The GCF is the largest number that divides both numbers without leaving a remainder.
To find the GCF of 18 and 27, we first need to find all factors of each number.
The factors of 18 are numbers that divide 18 evenly:
Factors of 18: 1, 2, 3, 6, 9, 18
Now we find all factors of 27:
Factors of 27: 1, 3, 9, 27
The common factors are numbers that appear in both lists:
Factors of 18: 1, 2, 3, 6, 9, 18
Factors of 27: 1, 3, 9, 27
Common factors: 1, 3, 9
The Greatest Common Factor is the largest of these: 9
We can also find the GCF using prime factorization:
Take the common prime factors with the lowest powers:
The Euclidean algorithm is a fast way to find the GCF using repeated division:
When the remainder is 0, the GCF is the last divisor: 9
GCF(18, 27) = 9