Question

Find the smallest 5 digit number which divided by 15,20,30and 35 leaves remainder 5 in each case

Answer 1

Answer:

When you divide 5 by any number ‘x’ that is larger than 5, you are asking how many times ‘x’ will go into 5. The quotient of 5/x when x > 5 is always zero, and the remainder is 5 for all positive x > 5

So the answer is: 5, which is the smallest number that has a remainder of 5 when divided by 15, 20, and 35.

We can find other larger integers that have a remainder of 5 when divided by 15, 20, and 25.

Using the J programming language, we can search all the integers up to 500:

(*./5=15 20 35 |/ i.500)#i.500

5 425

So there are only two integers between 1 and 500 that have a remainder of 5 when divided by 15, 20, and 35 - the original integer - 5 and the integer 425

15 20 35|425

5 5 5

Are their other integers, say up to 5000?

(*./5=15 20 35 |/ i.5000)#i.5000

5 425 845 1265 1685 2105 2525 2945 3365 3785 4205 4625

Yes, lots. But of course, 5 is the answer, as it is the smallest.