An easy question on divisibility and factors for P4–P5, with a step-by-step solution, diagrams and the answer. Common in the Hua Xia Cup's P4 and P5 qualifying rounds and finals; harder ones use how many factors a number has, and square numbers.
The question
A library book's number is a four-digit number, but one digit has been smudged with ink: all you can see is "4□28".
The librarian remembers that the number is divisible by 9.
What is the smudged digit?
Show the hints (2)
💡Hint 1: What do the three digits you can see add up to?
💡Hint 2: A number is divisible by 9 when its digits add up to a multiple of 9.
Worked solution
Have a go first, then read the solution step by step.
1.The digits you can see: 4 + 2 + 8 = 14.
2.A number divisible by 9 has a digit sum that is a multiple of 9.
3.14 + □ must be a multiple of 9, with □ from 0 to 9: 14 + 4 = 18, so □ = 4.
4.Check: 4428 ÷ 9 = 492.
⚠️Common mistake: thinking the digits must add up to exactly 9 — 18, 27 and other multiples of 9 work too.
Play more like this in Numsprite (unlimited questions, instant marking) →A free maths game: every level free from Easy to Expert (★ to ★★★★), unlimited questions, no download