# The Simplest Form of a Fraction

- Example:
- Find the simplest form of 30/45.

- Solution:
- A fraction is in simplest form when its numerator and denominator have no common factors other than 1.

- 30 = 1 × 30, 2 × 15, 3 × 10, 5 × 6
- Therefore, factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30.
- 45= 1 × 45, 3 × 15, 5 × 9
- Therefore, factor of 45 are 1, 3, 5, 9, 15, 45.
- The common factors of 30 and 45 are 1, 3, 5, 15.
- The greatest common factor (GCF) of 30 and 45 is 15.

- Note:
- When the numerator and denominator of a fraction divide by the greatest common factor (GCF), the fraction is the simplest form.