Threes and Fours
What is the smallest integer where every digit is a 3 or a 4 and it is divisible by both 3 and 4?
Age
14 to 16
Challenge level
Problem
An integer contains only the digits $3$ and $4$, with at least one of each.
The integer is divisible by both $3$ and $4$.
What is the smallest such integer?
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
Student Solutions
Answer: 3444
Digits add up to a multiple of 3
3 + 4 = 7 (at least one of each)
Adding more 3s will not help get closer to a multiple of 3
3 + 4 + 4 = 11
3 + 4 + 4 + 4 = 15
Smallest possibility: 3444
44 is divisible by 4 so 3444 is divisible by 4