Find the number (a positive integer), that gives the following values:?

Question

1) If you divide the number by 6, the reminder is 5
2) If you divide the number by 5, the remainder is 4
3) If you divide the number by 4, the remainder is 3
4) If you divide the number by 3, the remainder is 2
5) If you divide the number by 2, the remainder is 1

Find the lowest number (below 500) which meets the above criteria. Please explain how to get that number in least possible logical steps.

Answer 1

from 5, we know the number is odd, and from 2, the number can end in either 4 or 9, therefore ends in 9.

from 1, the division by 6 leaves a remainder of 5, which means that the number ending in 9 must be one below a multiple of 6 ==> 59.

Satisfies the others as well.

Answer 2

1) 11 (6 + 5)

2) 9 (5 + 4)

3) 7 (4 + 3)

4) 5 (3 + 2)

5) 3 (2 + 1)

i.e. Add both the numbers together, because you are dividing by the larger number you will always have the other number left as the remainder)

Answer 3

for all these numbers, it somehow turns that the remainder is "-1". ©

Get the LCM of 2 ... 6. .... Since "the number+1" is divisible by those numbers.
The LCM is 60.

The desired number is 60 -1 = 59.

59 = 6*9 + 5
59 = 5*11 + 4
59 = 4*14 + 3
59 = 3*19 + 2
59 = 2*29 + 1

Answer 4

Let x is the number to be find.

Hint:

The number (x+1) is divisible by 6, 5, 4, 3 and 2.

Now it's easy. Good luck.
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