Question

Find the greatest common factor of 18,36,54

a
9

b
12

c
18

Answer 1

To find the greatest common factor (GCF) of the numbers 18, 36, and 54, we can start by finding the prime factorization of each number:

- 18:
\( 18 = 2 \times 3^2 \)

- 36:
\( 36 = 2^2 \times 3^2 \)

- 54:
\( 54 = 2 \times 3^3 \)

Next, we identify the common prime factors and their lowest powers:

- For the prime factor 2, the lowest power among the numbers is \( 2^1 \).
- For the prime factor 3, the lowest power among the numbers is \( 3^2 \).

Now, we can multiply these together to find the GCF:

\[
\text{GCF} = 2^1 \times 3^2 = 2 \times 9 = 18
\]

Thus, the greatest common factor of 18, 36, and 54 is \( \mathbf{18} \).

The answer is **c) 18**.