Question

The numbers 1,3,5,….,25 are multiplied together. What is the number of zeros at the right end of the product?
(a) Zero
(b) 1
(c) 2
(d) 3

Answer 1

Hint:It is necessary to have a factor of 2 and 5 to get zero in the last of any number, like 20 can be represented as $2\times 2\times 5$ here we have both 2 and 5 as the factor of 20 and we are getting ‘0’ in last place of 20. We will check the same thing in given numbers to check zeros at the right end of the product.

Complete step-by-step answer:
It is given in the question that the number 1,3,5,7,….,25 are multiplied together, then we have to find the number of zeros at the right end of the product. But, if we notice the sequence given to us, then we observe that this series is a series of odd numbers from 1 to 25.
So, basically we are trying to find the product of odd numbers from 1 to 25 and at the end, we will check the number of zeros from right at the end of the product.
We know that it is necessary to have 2 and 5 as a factor of any number if the last digit ends with zero, like in 20, we have $2\times 2\times 5$, have $2\times 5$ as a factor then it has atleast one zero in the right side.
But, we know that 2 is an even number and we do not have $2\times 5$ as a factor of the product of odd numbers upto 25, thus, there will be no zeros in the end of the product of a given sequence.
Therefore, option a) is the correct answer.

Note: Many times students waste their time by actually multiplying all the numbers in the given series to check the number of zeros in the end. The chances of error are very high because we are multiplying many times to get the product. But, if we use our own knowledge, we can easily solve such questions in just a few steps.