Find the number of good numbers in the range 1 to 100 where a good number is a number that is multiple of both 3 and 7. Print all good numbers and the count of good numbers.
Find the number of good numbers in the range 1 to 100 where a good number is a number that is multiple of both 3 and 7. Print all good numbers and the count of good numbers.
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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Transcribed Image Text:**Problem Statement:**
Find the number of good numbers in the range 1 to 100 where a good number is a number that is a multiple of both 3 and 7. Print all good numbers and the count of good numbers.
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**Explanation:**
To solve this problem, we need to identify numbers between 1 and 100 that are multiples of both 3 and 7. A number that is a multiple of both 3 and 7 is a multiple of their least common multiple (LCM). Calculating the LCM of 3 and 7 gives us 21.
1. **Identify Good Numbers:**
- Find the multiples of 21 within the given range.
- Start from the smallest multiple of 21 greater than or equal to 1, which is 21 itself.
- Continue finding multiples by adding 21 repeatedly until the value exceeds 100.
2. **List of Good Numbers:**
- The good numbers between 1 and 100 are: 21, 42, 63, 84.
3. **Count of Good Numbers:**
- There are a total of 4 good numbers.
This exercise involves understanding how to leverage LCM to efficiently find common multiples, which is a fundamental concept in number theory and arithmetic.
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