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Determine the number of integers between 1 to 250 that are divisible by any of the integer 3 or 5 or 7?
Wiki User
∙ 13y ago
It would probably be easier to say that all numbers between 2 and 250 with the exception of the numbers 121, 143, 169 are divisible by the numbers 2,3,5, or 7.
Explanation:
One of the basic rules of math called the "Fundamental theorem of arithmetic" states that all numbers can be written as a product of prime numbers. 2, 3, 5, and 7 are the first four prime numbers.
We also know that at least one of the numbers multiplied has to be less then 16. This is because the square root of 250 is about 15.81. If more then one of the numbers were larger then 16, then the result would be greater then 250.
Example = 16*16 = 256.
So now we know that all numbers between 2 and 250 are divisible by prime numbers that are less then 16. These numbers are "2,3,5,7,11,13." If you notice the first four numbers in that list are the numbers that you gave.
This means that the only numbers between 2 and 250 that aren't divisible by 2, 3, 5, and 7 are the numbers (11*11), (11*13), and (13*13) or 121, 143, 169.
Wiki User
∙ 13y ago
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Determine the number of integers between 1 to 250 that are divisible by any of the integer 2 or 3 or 5 or 7?
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