Question

Find the greatest number of four digits which is exactly divisible by 12,16,28,24,36.

Answer 1

Let's look at the prime factors of the divisors:
12 = 2*2*3
16 = 2*2*2*2
24 = 2*2*2*3
28 = 2*2*7
36 = 2*2*3*3

So, the smallest number divisible by 12, 16, 24, 28 and 36 is
= (at least four multiples of 2's)*(at least two multiples of 3's)*(at least one multiple of 7)
= (2 * 2 * 2 * 2) * (3 * 3) * (7)
= 1008

The greatest 4-digit number available is 9999.

9999/1008 = 9.9196...
[NOTE: The quotient is 9, while the remainder is 1008*0.9196.. ]

Therefore, the greatest 4-digit number divisible by 12, 16, 24, 28 and 36 is
= 9*1008
= 9072

Answer 2

The no. Is 1008

Hope it will help