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31 May 2010, 11:18
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They say that 3 consecutive integers will have a multiple of 3.
What about 0, 1, 2 ??? No multiples of 3 there.
What about 0, 1, 2 ??? No multiples of 3 there.
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31 May 2010, 16:17
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You've forgotten 0--it is a multiple of three, though many people forget it!
You know the multiples of 3 all differ by 3: 3, 6, 9, 12, 15, etc.
There are negative multiples of 3, which all differ by 3, too: -3, -6, -9, -12, -15, etc.
We can't skip from -3 to 3! Zero, like all other multiples of 3, differs from the neighboring multiples by 3.
Another way to remember this special case: we test whether a number is a multiple by dividing it to see if we get an integer. For example, we know 18 is a multiple of 3 because 18/3 = 6, an integer. But 17 is not a multiple of 3 because 17/3 = 5.667, a non-integer. Test zero the same way: 0/3 = 0, an integer.
More general rule: 0 is divisible by ALL non-zero integers.
You know the multiples of 3 all differ by 3: 3, 6, 9, 12, 15, etc.
There are negative multiples of 3, which all differ by 3, too: -3, -6, -9, -12, -15, etc.
We can't skip from -3 to 3! Zero, like all other multiples of 3, differs from the neighboring multiples by 3.
Another way to remember this special case: we test whether a number is a multiple by dividing it to see if we get an integer. For example, we know 18 is a multiple of 3 because 18/3 = 6, an integer. But 17 is not a multiple of 3 because 17/3 = 5.667, a non-integer. Test zero the same way: 0/3 = 0, an integer.
More general rule: 0 is divisible by ALL non-zero integers.
