false
Catalog
Grades 11-12 Video Solutions 2014
11&12 Video Solutions 2014 problem25
11&12 Video Solutions 2014 problem25
Back to course
[Please upgrade your browser to play this video content]
Video Transcription
Video Summary
Tom can write up to 69 distinct positive integers without exceeding 100, ensuring their product is not divisible by 54. To achieve this, he avoids numbers divisible by 3, leaving 67 potential factors. He can then add two numbers divisible by 3, such as 3 and 6, without the product being divisible by 54. This ensures their product adheres to the condition by only being divisible by \(2 \times 3^2\) and not \(2 \times 3^3\), making 69 the maximum count of integers he can write without violating the divisibility rule.
Keywords
distinct integers
divisibility
product rule
positive integers
maximum count
×
Please select your language
1
English