### Brain Teasers

# Threes and Sevens 2

Which is the smallest natural number that satisfies the following conditions:

(1) Its digits consist of, and only of 3's and 7's.

(2) Its digital sum is divisible by 3 and 7.

(3) The number itself is divisible by 3 and 7.

(1) Its digits consist of, and only of 3's and 7's.

(2) Its digital sum is divisible by 3 and 7.

(3) The number itself is divisible by 3 and 7.

### Hint

It's not very hard.### Answer

From conditions 1 and 2, we know that we need at least 3 7's and 7 3's.Their sum is divisible by 3, therefore any number they make is divisible by 3.

By trial and error, we see that none of 3333333777, 3333337377, 3333337737, 3333337773, 3333373377, 3333373737, 3333373773, 3333377337 and 3333377373 is divisible by 7.

3333377733 is divisible by 7 (the quotient is 476196819.)

Therefore, the number we're looking for is 3333377733.

Hide Hint Show Hint Hide Answer Show Answer

## What Next?

View a Similar Brain Teaser...

If you become a registered user you can vote on this brain teaser, keep track of which ones you have seen, and even make your own.

### Solve a Puzzle

Comments hidden to avoid spoilers.

## Follow Braingle!