Only three whole numbers exist such that the digits from lef

Only three whole numbers exist such that the digits from left to right are consecutive integers in increasing order and the number is divisible by 24. Find the three numbers.

Solution

Multiple of 24 => 2,3,4,6,8 are factors

The first among them with consecutive digits and factor of 24 will be a 3 digit no

Digits are x-1,x,x+1

Since 2 is a factor x+1 = one of 2,4,6,8 however as x+1 is the greatest of all, the only possibilities are 678,456,234 out of which only 456 is a multiple of 24

Next let us consider 4 digit no with digits x-2,x-1,x,x+1 again possibilities are 5678, 3456, 1234 out of which only 3456 is a multiple of 24

Next let us consider 5 digit no with digits x-3,x-2,x-1,x,x+1 again possibilities are 45678, 23456 out of which no multiples of 24

Next let us consider 6 digit no where possibilities with 2 as factor are 123456, 345678 where 123456 is a multiple of 24

Ans

456

3456

123456