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:
\(720n ≤ 9999 → n ≤ \frac{9999}{720} → n ≤ 13.8875 → n = 13 →
720n = 9360\)
Reza is an experienced Math instructor and a test-prep expert who has been tutoring students since 2008. He has helped many students raise their standardized test scores--and attend the colleges of their dreams. He works with students individually and in group settings, he tutors both live and online Math courses and the Math portion of standardized tests. He provides an individualized custom learning plan and the personalized attention that makes a difference in how students view math.
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