Question

Replace the symbols * and # in 9586*4# so that it is divisible by both 8 and 5.

Answer 1

for the divisibility with 5 # should be 0 or 5 and for divisibility with 8 *4# should be divisible by 8

Answer 2

Concept:

In mathematics, divisibility tests or division rules allow you to determine whether a number is divisible by another integer without having to use the division technique. The quotient will be a whole number and the remainder will be zero if a number is totally divisible by another integer.

Given:

The number 9586*4#.

It should be divisible by both 5 and 8.

Find:

The digits that should be placed in * and # places in order to be divisible by both 5 and 8.

Solution:

In order to be divisible by 5, the last digit of the number must end with 0 or 5.

In the case of divisibility of 8, the last three digits of the number should be divisible by 8.

If we place 0 in #. Then, the possible last three-digit numbers are 040, 140, 240, 340, 440, 540, 640, 740, 840, 940.

From this list of numbers, only 5 numbers are divisible by 8 (040, 240, 440, 640, 840).

If we place 5 in #. Then, the possible last three-digit numbers are 045, 145, 245, 345, 445, 545, 645, 745, 845, 945.

No number is divisible by 8 from this list of numbers.

Hence, the possible digit in # is 0, and in place * it can have 0,2,4,6 and 8 digits.