Count of Multiples of 2 or 7 in 999

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In summary, in order to find the count of multiples of 2 or 7 for all natural numbers less than or equal to 999, we first calculate the number of multiples of 2 and 7 separately, which are 499 and 142 respectively. However, since this includes the multiples of 14 being counted twice, we need to subtract the number of multiples of 14 (71) from the total count (641) to get the final answer of 570.
  • #1
sabsac
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Find the count of multiples of 2;or 7, for all natural numbers less than or equal to 999.
 
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  • #2
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= [FONT=Verdana,Arial,Tahoma,Calibri,Geneva,sans-serif]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.[/FONT]
 
  • #3
the answer provided is 570 which is the difference between 641 and 71. that difference between the total count of multiples of 2 and 7.
 
  • #4
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.
Mathematicians often have trouble with simple arithmetic! :rolleyes:
 
  • #5
so can you once again explain how we arrived at the value 71 and why we had to subtract it from 641?
 
  • #6
multiples of 2 less than 999 ...

2(1), 2(2), 2(3), ... , 2(499)

multiples of 7 less than 999 ...

7(1), 7(2), 7(3), ... , 7(142)

multiples of 14 less than 999 which are common to both lists above ...

14(1), 14(2), 14(3), ... , 14(71)
number of multiples of 2 or 7 that are less than 999 =

(multiples of 2)+(multiples of 7)-(number of values that are multiples of both 2 and 7) =

499+142-71
 
  • #7
Thanks for clarifying.
 

Related to Count of Multiples of 2 or 7 in 999

What is the Count of Multiples of 2 or 7 in 999?

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.

How do you calculate the Count of Multiples of 2 or 7 in 999?

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.

What is the difference between multiples of 2 and multiples of 7 in 999?

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.

How does the Count of Multiples of 2 or 7 change if the range is extended to 1999?

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.

Are there any other numbers that can be used to calculate the Count of Multiples of 2 or 7 in a given range?

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.

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