Find the largest multiple of 2, 3 and 5

An array of size n is given. The array contains digits from 0 to 9. Generate the largest number using the digits in the array such that the number is divisible by 2, 3 and 5.
For example, if the arrays is {1, 8, 7, 6, 0}, output must be: 8760. And if the arrays is {7, 7, 7, 6}, output must be: “no number can be formed”.

Source: Amazon Interview | Set 7

This problem is a variation of “Find the largest multiple of 3“.

Since the number has to be divisible by 2 and 5, it has to have last digit as 0. So if the given array doesn’t contain any zero, then no solution exists.

Once a 0 is available, extract 0 from the given array. Only thing left is, the number should be is divisible by 3 and the largest of all. Which has been discussed here.



Thanks to shashank for suggesting this solution. Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.

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