Give it a thought!
Number Theory
Level
2
Find smallest positive integer such that it is a multiple of 9 and it has no odd digits.
The answer is 288.
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
1 solution
For a number be multiple of 9 it s sum of digits must be multiple of 9.as 9 is an odd number and the question request that all the numbers must be an even number,the nunber we are looking for cannot has the sum of digits equal to 9 cuz, for parity,the sum of even number cannot be equal to a odd number So the number we are looking for must has the sum equal to 18 cuz this is a multiple of 9.as it has to be the least, it must has the minimum number of digits.as neither with 2 digits nor with 1its possible to get a sum of even numbers equal to 18,it must has 3 number.8+8+2=18, as it must be the least is 288