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napy27
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If x is an even integer, is x(x+1)(x+2) divisible by 4? 11 May 2011, 09:39
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If x is an even integer, is x(x+1)(x+2) divisible by 4?

According to MGMAT, the answer is yes and I believe for all cases it is except I'm curious about one situation. If x is 0, would the product (0*1*2=0) be considered divisible by 4?
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If x is an even integer, is x(x+1)(x+2) divisible by 4? 11 May 2011, 09:49
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napy27
If x is an even integer, is x(x+1)(x+2) divisible by 4?

According to MGMAT, the answer is yes and I believe for all cases it is except I'm curious about one situation. If x is 0, would the product (0*1*2=0) be considered divisible by 4?

0 is divisible by all real numbers but 0 itself.
0 is a multiple of all real numbers.

So yes, 0 is definitely divisible by 4.

Please visit math-number-theory-88376.html for a concise yet complete summary of number properties.
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If x is an even integer, is x(x+1)(x+2) divisible by 4? 11 May 2011, 11:19
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Yeah, 0 is divisible by all real numbers except itself.

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If x is an even integer, is x(x+1)(x+2) divisible by 4? 11 May 2011, 21:11
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divisible under all the cases for both positive and negative even integers and 0 too.

x+2 makes the number divisible by 4.
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If x is an even integer, is x(x+1)(x+2) divisible by 4? 24 Mar 2020, 02:08
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but what if x =21, is it still divisible by 4
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If x is an even integer, is x(x+1)(x+2) divisible by 4? 24 Mar 2020, 02:14
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gagan543
but what if x =21, is it still divisible by 4

It's not clear what you are trying to say. Also, notice that we are given that x is an even integer: If x is an even integer, is x(x+1)(x+2) divisible by 4? 21 is odd, not even. And finally, if x = 21, then x(x+1)(x+2) is NOT divisible by 4.
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If x is an even integer, is x(x+1)(x+2) divisible by 4? 24 Mar 2020, 08:20
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napy27
If x is an even integer, is x(x+1)(x+2) divisible by 4?

According to MGMAT, the answer is yes and I believe for all cases it is except I'm curious about one situation. If x is 0, would the product (0*1*2=0) be considered divisible by 4?

Let x = 2k : where k is an integer
x(x+1)(x+2) = 2k(2k+1)(2k+2) = 4k(k+1)(2k+1) ; Divisible by 4
It does not matter whether x = 0 or not
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