# 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.

Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.

## Recommended Posts:

- Find the largest multiple of 3 | Set 1 (Using Queue)
- Find the largest multiple of 3 from array of digits | Set 2 (In O(n) time and O(1) space)
- Find the multiple of x which is closest to a^b
- Find First element in AP which is multiple of given prime
- Find multiple of x closest to or a ^ b (a raised to power b)
- Find the largest twins in given range
- Find largest number smaller than N with same set of digits
- Find largest prime factor of a number
- Legendre's formula (Given p and n, find the largest x such that p^x divides n!)
- Find Largest Special Prime which is less than or equal to a given number
- Find the area of largest circle inscribed in ellipse
- Find the original matrix when largest element in a row and a column are given
- Find the Largest Cube formed by Deleting minimum Digits from a number
- Find the largest good number in the divisors of given number N
- Multiple of x closest to n