How to calculate the number of numbers within a given range having prime factor as 3 and 5

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1

how to calculate the number of numbers within a given range having prime factor as 3 and 5

2

To calculate the number of numbers within a given range that have either 3 or 5 as their prime factor, you can follow these steps:

  1. Identify the given range (L to R, where L is the lower limit and R is the upper limit).
  2. Loop through the numbers within the range and check if each number has either 3 or 5 as its prime factor.
  3. Count the numbers that meet the condition.
  4. Output the count as the final result.
3 
int fifteen_count = R/15 - (L+14)/15 + 1;
int three_count = R/3 - (L+2)/3 + 1;
int five_count = R/5 - (L+4)/5 + 1;
int answer = five_count + three_count - fifteen_count;

For example, if L = 2 and R = 18
fifteen_count = 1 - 1 + 1 = 1
three_count = 6 - 1 + 1 = 6
five_count = 3 - 1 + 1 = 3
answer = 6 + 3 - 1 = 8

Note that this is correct because the numbers in the range [2,18] divisible by 3 or 5 are
3, 5, 6, 9, 10, 12, 15, 18

4

Hello this is Gulshan Negi
Well, I searched about it on the Internet and I found that you can follow the below steps to do this.

  1. Define the given range: Determine the lower and upper limits of the range for which you want to find the numbers with 3 and 5 as prime factors.

  2. Loop through the numbers in the given range: Start iterating through the numbers in the given range, checking each number to see if it has 3 and 5 as prime factors.

  3. Check for prime factors: For each number in the range, check if it is divisible by 3 and 5 without any remainder. You can use the modulo operator (%) to check for divisibility.

  4. Count the numbers with prime factors: If a number in the range is divisible by both 3 and 5, increment a counter to keep track of the numbers that have 3 and 5 as prime factors.

  5. Repeat for all numbers in the range: Continue the loop until you have checked all the numbers in the given range.

  6. Output the result: After checking all the numbers, the counter will contain the count of numbers that have 3 and 5 as prime factors. You can output this count as the final result.

I hope it is clear now.
Thanks

5

For example, if the range is from 1 to 100, there are 6 multiples of 15 in the range (15, 30, 45, 60, 75, and 90), so the number of numbers within the given range having prime factors as 3 and 5 is 6.