- #1
sabsac
- 4
- 0
Find the count of multiples of 2;or 7, for all natural numbers less than or equal to 999.
Mathematicians often have trouble with simple arithmetic!HallsofIvy said:There are integer part of 999/2= 499 even numbers les than or equal to 999. There are integer part of 999/7= 142 multiples of 7 less than or equal to 999. But 499+ 142= 1141 is too larger because it counts multiples of 14 twice. We need to subtract integer part of 999/14= 71 to account for that.
The count of multiples of 2 or 7 in 999 is 142. This means that there are 142 numbers between 1 and 999 that are divisible by either 2 or 7.
To calculate the count of multiples of 2 or 7 in 999, you can use the following formula:
Count = floor(999/2) + floor(999/7) - floor(999/14)
This formula takes into account the multiples of both 2 and 7, while subtracting the common multiples of 2 and 7 (i.e. multiples of 14) to avoid double counting.
The difference between multiples of 2 and multiples of 7 in 999 is that multiples of 2 occur more frequently than multiples of 7. This is because 2 is a smaller number and has more factors, making it easier to have multiples. In contrast, 7 is a larger number and has fewer factors, making it less likely to have multiples.
If the range is extended to 1999, the count of multiples of 2 or 7 will increase to 284. This is because there are more numbers between 1 and 1999 that are divisible by either 2 or 7, compared to 999.
Yes, there are other numbers that can be used to calculate the Count of Multiples of 2 or 7 in a given range. Some examples include the least common multiple (LCM) of 2 and 7, as well as the product of 2 and 7. However, the formula mentioned in the second question is the most commonly used method.