Given
We are to find the Greatest Common Factor of 90, 135 and 225
First, we should decompose all numbers into their prime factors and write them as a product
[tex]\begin{gathered} 90\text{ = 2 }\times3\text{ }\times\text{ 3 }\times\text{ 5} \\ 135\text{ = }3\text{ }\times\text{ 3 }\times\text{ 3 }\times\text{ 5} \\ 225\text{ = }3\text{ }\times\text{ 3 }\times\text{ }5\text{ }\times\text{ 5} \end{gathered}[/tex]Then we choose the common prime factors: 3, 3 and 5
The greatest common factor (GCF) is obtained by multiplying the common prime factors:
[tex]\begin{gathered} \text{GCF = }3\text{ }\times\text{ 3 }\times\text{ 5} \\ =\text{ 45} \end{gathered}[/tex]Hence, the GCF is 45.
Answer: 45
