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Which number is divisible by 2 and 9 that is in between 424 and 449?
Numbers divisible by 9 have the sum of their digits equal to 9 or a multiple of 9. A number divisible by 2 is an even number. If a 3 digit number is 42n then n can only be 3 if the number is divisible by 9 and 423 is not within the specified range. If a 3 digit number is 43n then n must be 2 for it to be divisible by 9.. The number is thus 432 and this is even and so divisible by 2. If the 3 digit number is 44n then n must be 1 and 441 is odd and not divisible by 2. The only valid solution is 432.
Why the divisibility test for 9 is valid and a way to determine whether a three-digit counting number ABC is divisible by 9?
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How many 10-digit positive integers with distinct digits are multiples of 11111?
-11101
Prove that one of every 3 consecutive positive integers is divisible by 3?
Let three consecutive integers be n, n+1 and n+2. If n is divisible by 3 then n+1 and n+2 cannot be divisible by 3 as these numbers will respectively leave remainders of 1 and 2. If n is not divisible by 3 then it will leave a remainder of 1 or 2. If n leaves a remainder of 1, then n+1 leaves a remainder of 2 and n+2 is therefore divisible by 3. If n leaves a remainder of 2, then n+1 is divisible by 3 and n+2 is not divisible by 3 as it leaves a remainder of 1.
Prove that the two consecutive positive integer is divisible by 2?
There is something missing from your question: what about the two consecutive integers? Is the proof required that one of them is divisible by 2? Or that their product is (which amounts to the same thing)? Showing that one of two consecutive number is divisible by 2: Suppose your two numbers are n and (n+1). If n is divisible by 2, ie n = 2k, the result is shown. Otherwise assume n is not divisible by 2. In this case n = 2m+1. Then: (n+1) = ((2m+1)+1) = 2m + 2 = 2(m+1) which is a multiple of 2 and so divisible by 2. QED. Showing that exactly one of two consecutive integers is divisible by two is shown above with the addition to the first part: "as (n+1) = 2k+1 is not divisible by two and so only n is divisible by 2." To show the product is divisible by 2, show either n is divisible by 2 or (n+1) is as above, then the result follows as one of n and (n+1) is divisible by 2 and so their product is.
