To simplify the fraction [tex]\(\frac{15}{27}\)[/tex] to its lowest terms, you need to find the greatest common factor (GCF) of both the numerator (15) and the denominator (27).
Here is a step-by-step method to find the GCF and simplify the fraction:
1. List the factors: Find all the factors of the numerator and the denominator.
- Factors of 15: 1, 3, 5, 15
- Factors of 27: 1, 3, 9, 27
2. Identify the common factors: Determine which factors are common to both numbers.
- Common factors of 15 and 27: 1, 3
3. Select the greatest common factor: Among the common factors, the greatest one is:
- The greatest common factor (GCF) is 3.
4. Simplify the fraction: Divide both the numerator and the denominator by their GCF.
- Numerator: [tex]\( \frac{15}{3} = 5 \)[/tex]
- Denominator: [tex]\( \frac{27}{3} = 9 \)[/tex]
So, the simplified fraction of [tex]\(\frac{15}{27}\)[/tex] is [tex]\(\frac{5}{9}\)[/tex].
Therefore, the greatest common factor (GCF) of 15 and 27 is 3, and the fraction simplifies to [tex]\(\frac{5}{9}\)[/tex].
