Other Topics Puzzle – Challenge 99
This cool puzzle (and solution) can help you challenge your students. It only requires basic knowledge of mathematics. Let's see who can solve it!
Challenge:
Find the highest four-digit number that is divisible by each of the numbers 16, 36, 45, and 80.
The Absolute Best Book to Challenge Your Smart Student!
The correct answer is 9360.
For a positive integer to be divisible by those numbers, it must be divisible by their Least common multiple:
Factorize the numbers to find their Least Common Multiple.
\(16 = 2^4\)
\(36 = 2^2 × 3^2\)
\(45 = 3^2 × 5\)
\(80 = 2^4 × 5\)
Least Common Multiple \(= 2^4 × 3^2 × 5 = 720\)
Every multiple of 720 is divisible by all those above.
Every multiple of 720 can be written as 720n, where n is an integer. The largest 4-digit integer is 9999. Therefore:
\(720n ≤ 9999 → n ≤ \frac{9999}{720} → n ≤ 13.8875 → n = 13 →
720n = 9360\)
The Best Books to Ace Algebra
Related to This Article
More math articles
- How to Simplify Radical Expressions Involving Fractions?
- Building with Blocks: How to Multiply Decimals by 1-digit Whole Numbers
- How is the SSAT Test Scored?
- How to Solve Exponential Equations?
- How to Solve Word Problems of Counting Bills and Coins
- Top 10 7th Grade PARCC Math Practice Questions
- 4th Grade PSSA Math Practice Test Questions
- A Guide to the Key Properties of Integrals
- Best Smartphones for Math Teachers
- A Comprehensive Collection of Free ASVAB Math Practice Tests
What people say about "Other Topics Puzzle – Challenge 99 - Effortless Math: We Help Students Learn to LOVE Mathematics"?
No one replied yet.