Divisibility question?

Question

What is the greater number that consists of only distinct digits and is divisible by 5, 8 and 11? It's best if you give reasoning/proof yours is the correct answer...

Of course it should have been "greatest", not greater...

@sarkartapas2005: Don't tell me my question is wrong! How do you know that?

Answer 1

Number has at most 10 digits lest two be equal. Multiple of
5 but not 25 to give only one zero on the right. Go with
987654abcd. divisibility by 11 gives 9+7+5+a+c minus
8+6+4+b+d a multiple of 11, so 3+a+c-b-d where d=0
11 divides3+a+c-b using 1,2,3 leaves only 1320 which
fails to give number divisible by 440 so 4 is in the wrong place. 9876513240 is divisible by 440 and permuting 13240 must preserve divisibility by 11 which doesn't happen so
N = 9876513240. This is the largest number with all digits distinct and divisible by 440.

Answer 2

Hello

The smallest number that consists of distinct 5, 8 and 11 is 440.

The hardest part of this is finding a multiple of 11 that is divisible by 8 and 5.

This happens when 11 is multiplied by a multiple of 8 (as well as 5).

Thus 11 * 40 = divisible by 8 & 5
also 11 * 80 = divisible by 8 & 5
also 11 * 120= divisible by 8 & 5
also 11 * 160 = divisible by 8 & 5

Thus we get 11 * {(8*5)(n)}. Let n = positive integer.
Simplifying this and we get 440n. So the greastest would be infinity.

Answer 3

Your question is wrong.It should have been "What is the least number that.....by 5,8 and 11?"
Well the least number is the LCM of 5,8 and 11 and as there is no common factor the LCM is naturally 5*8*11=440.
All multiples of 440 is divisible by 5,8 and 11 and if we have to find the greater numbers as per your question,then we shall have innumerable ones which satisfy the problem

Answer 4

There is no common factors between 5, 8 and 11 so the answer is
5x8x11=440