GCF of 14 and 21
Find the Greatest Common Factor (GCF) of 14 and 21 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 14 and 21, we first need to find all factors of each number.
The factors of 14 are numbers that divide 14 evenly:
Factors of 14: 1, 2, 7, 14
Now we find all factors of 21:
Factors of 21: 1, 3, 7, 21
The common factors are numbers that appear in both lists:
Factors of 14: 1, 2, 7, 14
Factors of 21: 1, 3, 7, 21
Common factors: 1, 7
The Greatest Common Factor is the largest of these: 7
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: 7
GCF(14, 21) = 7