disibilityruleof2,3,4,5,6,7,9and10
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Answer:
What number is divisible by 2,3,4,5,6,7,8,9 and 10?
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James Durdan
Answered 2 years ago · Author has 1.1K answers and 1.6M answer views
Every number is divisible by the numbers 2, 3, 4, 5, 6, 7, 8, 9, 10 (the “Nine Numbers”). However, not all numbers are EVENLY divisible by the Nine Numbers. I assume you mean evenly divisible.
The Smallest Positive Number Evenly Divisible
To be evenly divisible by all of the Nine Numbers, a number would need to include the following prime number factors and in the quantities indicated:
one factor of 7 (or it wouldn’t be divisible by 7);one factor of 5 (or it wouldn’t be divisible by 5 or 10),two factors of 3 (otherwise not divisible by 9); andthree factors of 2 (otherwise not divisible by 8).
In other words, it would need to be:
2 * 2 * 2 * 3 * 3 * 5 * 7 = 2,520.
That is, of course, the smallest positive number divisible by all of the Nine Numbers.
Other Numbers Evenly Divisible
Any number obtained using the formula:
N = 2,520 * n for any integer n (including negative integers)
will also be evenly divisible by the Nine Numbers.
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