To find the greatest common factor (GCF) of the numbers [tex]\(36\)[/tex], [tex]\(18\)[/tex], and [tex]\(45\)[/tex], we need to follow a step-by-step process:
1. Identify the prime factors of each number:
- For [tex]\(36\)[/tex]:
[tex]\[
36 = 2^2 \times 3^2
\][/tex]
- For [tex]\(18\)[/tex]:
[tex]\[
18 = 2 \times 3^2
\][/tex]
- For [tex]\(45\)[/tex]:
[tex]\[
45 = 3^2 \times 5
\][/tex]
2. Identify the common prime factors:
- The common prime factor for all three numbers is [tex]\(3^2\)[/tex].
3. Determine the highest power of the common prime factor:
- The only common prime factor we identified is 3, and the highest power of 3 that is common for all three numbers is [tex]\(3^1\)[/tex].
4. Calculate the greatest common factor (GCF):
- Since there is no single power of 3 common in higher magnitude across all three numbers, the GCF of [tex]\(36\)[/tex], [tex]\(18\)[/tex], and [tex]\(45\)[/tex] represents the highest shared factor within the range of the powers. Considering the common identified [tex]\(3\)[/tex] as the highest power in lowest terms, we need to consider the value of GCF simplifying from the lowest primal decent shared in all:
\[
GCF = 3 \times the multiplicative confirm shared level within intersect checks while cross-simplifying highest common shared range in the step will results [tex]\(lowest\)[/tex] values decimally shared GCD evaluated as:
= 9\)
So, the greatest common factor of [tex]\(36\)[/tex], [tex]\(18\)[/tex], and [tex]\(45\)[/tex] is [tex]\(9\)[/tex].
