Question

3) By how many zeros do the following numbers end:a) 7^2 × 2^4 × 5^4 b) 3^5 × 2^7 × 11^2 × 5^6

Answer 1

(3). (a) We want to find the number of zeros the number

72 × 24 × 54 end.

To do this, what we have to do is count how many times did 2 and 5 occurred in the question as factor. Number of zeros is equal to the one (2 or 5) which occurred less times.

From7^2 × 2^4 × 5^4, we have

`\begin{gathered} 7^2\text{ there are no 5's or 2's} \\ 2^4,\text{ there are four 2's} \\ 5^4,\text{ there are four 5's } \\ Altogether,\text{ we have four 2's and four 5's} \\ So,\text{ since the number of 2's and 5's are equal, we choose one} \end{gathered}`

Hence the answer is 4 zeros

(b) 3^5 × 2^7 × 11^2 × 5^6

`\begin{gathered} 3^5,\text{ there are no 2's or 5's } \\ 2^7,\text{ there are seven 2's} \\ 11^2,\text{ there are no 2's or 5's} \\ 5^6,\text{ there are six 5's} \\ Making\text{ a total of seven 2's and six 5's. So we go for the lesser} \\ which\text{ is six 5's } \end{gathered}`

Hence the answer is 6 zeros