What is the greatest possible common divisor of two : PS Archive
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# What is the greatest possible common divisor of two

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What is the greatest possible common divisor of two [#permalink]

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15 Mar 2006, 21:23
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What is the greatest possible common divisor of two different positive integers which are less than 144?

143
142
72
71
12
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15 Mar 2006, 21:33
We can take out 143 and 142 because they are too large to be the divisor of any 2 numbers below 144.

72 is also out as the second multiple of 144 and we need the number to be below 144.

71 is the best choice.

I'll take D
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16 Mar 2006, 08:30
144/2 = 72.

It has to be less than 72.
Should be 71.
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16 Mar 2006, 10:12
Riuscita, I had problems really understanding the concept to this one when I first saw it in the Kaplan book. But the concept is easier to comprehend if you look at it backwards.

In order for a number to be the greatest common divisor for two different positive integers that are less than 144, we need to be able to multiply that number with two different positive integers and still get a result that is less than 144.

143 * 1 = 143; 143 * 2 = .... obviously this would be greater than 144. No need to calculate.

142 * 1 = 142; 142 * 2 = .... same as above

72 * 1 = 72; 72 * 2 = 144 .... 144 is not less than 144.

71 * 1 = 71; 71 * 2 = 142 .... eureka! there we have it...

16 Mar 2006, 10:12
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