Division 40223C

1. **State the problem:** We need to divide $20625$ by $60$. 2. **Formula used:** Division is the operation of determining how many times one number is contained within another. The formula is $$\text{Quotient} = \frac{\text{Dividend}}{\text{Divisor}}$$ where the dividend is $20625$ and the divisor is $60$. 3. **Perform the division:** $$\frac{20625}{60}$$ 4. **Simplify the fraction:** First, find the greatest common divisor (GCD) of $20625$ and $60$. - Prime factors of $20625$: $3 \times 5^4 \times 11$ - Prime factors of $60$: $2^2 \times 3 \times 5$ Common factors: $3$ and $5$ GCD is $3 \times 5 = 15$ 5. **Divide numerator and denominator by GCD:** $$\frac{\cancel{15} \times 1375}{\cancel{15} \times 4} = \frac{1375}{4}$$ 6. **Convert to mixed number or decimal:** $$1375 \div 4 = 343 \text{ remainder } 3$$ So, $$\frac{1375}{4} = 343 \frac{3}{4} = 343.75$$ **Final answer:** $$20625 \div 60 = 343.75$$