Question

Which of the following is a product of 17 and an integer?
(a) 171
(b) 1712
(c) 1724
(d) 1734

Answer 1

Hint: First of all try to recollect what an integer is. Then divide each of the options by 17 and check in which of them the quotient is coming as integer and that will be your answer.

Complete step-by-step answer:
We are given a number 17 and we have to check which numbers are the product of 17 and an integer out of 171, 1712, 1724, and 1734. First of all, we must know what an integer is. An integer is a number that is not a fraction or which has no fractional part. In other words, it is a number as a whole. For example, – 1, 0, 1, 2, 225, – 11 are integers.
Now, to check which numbers are the product of 17 and an integer, we will divide each number by 17 and check the quotient for integers. The numbers for which quotient would be integer will be the product of 17 and an integer.
Let us consider option (a) 171. By dividing 171 by 17, we get

As we can see that here quotient = 10.05 is not an integer, therefore this is not our answer.
Let us consider option (b) 1712. By dividing 1712 by 17, we get

As we can see that here quotient = 100.7 is not an integer, therefore this is not our answer.
Let us consider option (c) 1724. By dividing 1724 by 17, we get

As we can see that here quotient = 101.4 is not an integer, therefore this is not our answer.
Let us consider option (d) 1734. By dividing 1734 by 17, we get

As we can see that here quotient = 102 is an integer, therefore this is our answer.
We can write 1734 as a product of 17 and an integer. That is 1734 = 17 x 102.
Hence, option (d) is the right answer.

Note: Students must note that whenever a number is a product of two integers, then that two integers are factors of that number, or in other words, we can say that these integers would divide that number wholly. For example, we have 1734 = 17 x 102. This means that 17 and 102 are factors of 1734 and when we will divide 1734 by 17, we will get a whole number 102 and when we will divide 1734 by 102, we will get number 17.