how to calculate the number of numbers within a given range having prime factor as 3 and 5
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:
- Identify the given range (L to R, where L is the lower limit and R is the upper limit).
- Loop through the numbers within the range and check if each number has either 3 or 5 as its prime factor.
- Count the numbers that meet the condition.
- Output the count as the final result.
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
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.
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.
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.
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.
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.
Repeat for all numbers in the range: Continue the loop until you have checked all the numbers in the given range.
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.
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.