AP EAMCET · Maths · Binomial Theorem
The greatest integer \(\mathrm{r}\) such that \(30^{\mathrm{r}}\) divides 30 ! is
- A \(8\)
- B \(7\)
- C \(6\)
- D \(5\)
Answer & Solution
Correct Answer
(B) \(7\)
Step-by-step Solution
Detailed explanation
Since \(30^{\mathrm{r}}\) divides \(30 !\) Now \(30^{\mathrm{r}}=2^{\mathrm{r}} \times 3^{\mathrm{r}} \times 5^{\mathrm{r}}\) Since 5 divides 30 ! So \(r=\left[\frac{30}{5}\right]+\left[\frac{30}{5^2}\right]=6+1=7\)
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