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Number Properties

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by gmat_chanakya » Wed Mar 26, 2014 8:19 pm
This question has kept me occupied for the entire day. I am trying to arrive at a general concept here, if anyone could help me.

"If a number Z is divisible by X, when would it also be divisible by Y" ?

For Example: the number 108 is divisible by 27 and also divisible by 54. When would a number be divisible by both 27 and 54 ? What's the general concept hidden behind this problem that GMAT would try to test ?

A similar question to think about is " Would three consecutive integers be divisible by both 27 and 54" ?

The answer to this would help to solve several GMAT problems quicker. There is something it has got to do with the factors, but I just can't get clarity.

Any help would be appreciated.
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by [email protected] » Wed Mar 26, 2014 11:42 pm
Hi gmat_chanakya,

The concept that you've mentioned in this post is ultimately about "prime factorization" - by knowing what prime factors divide evenly into a number, you can figure out all of the possible values that can divide evenly into that number.

For example, the number 20 = 2x2x5

This means that the following numbers will divide evenly into 20:
1
2
4 = 2x2
5
10 = 2x5
20 = 2x2x5

This rule tends to come in handy when dealing with really big numbers or when trying to figure out the values at which numbers overlap with one another.

For example, what's the least common multiple of 4 and 6?

4 = 2x2
6 = 2x3

Notice how BOTH terms includes a "2"? In this scenario, you DON'T count that 2 twice.

The LCM of 4 and 6 = 2x2x3 = 12

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Rich
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by Brent@GMATPrepNow » Thu Mar 27, 2014 7:32 am
gmat_chanakya wrote:This question has kept me occupied for the entire day. I am trying to arrive at a general concept here, if anyone could help me.

"If a number Z is divisible by X, when would it also be divisible by Y" ?

For Example: the number 108 is divisible by 27 and also divisible by 54. When would a number be divisible by both 27 and 54 ? What's the general concept hidden behind this problem that GMAT would try to test ?

A similar question to think about is " Would three consecutive integers be divisible by both 27 and 54" ?

The answer to this would help to solve several GMAT problems quicker. There is something it has got to do with the factors, but I just can't get clarity.

Any help would be appreciated.
Here's one possible way to complete your general concept (i.e., "If a number Z is divisible by X, when would it also be divisible by Y?"):

We can write: If integer X is divisible by integer Y, then the following rule applies: If integer Z is divisible by X then Z is also divisible by Y.

For example, 32 is divisible by 16. So, if 544 is divisible by 32 then 544 is also divisible by 16

Is this the kind of thing you're looking for?

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by gmat_chanakya » Thu Mar 27, 2014 2:42 pm
Thank you Rich.C and Brent!
The prime factorization method was the one I was trying to get hold of and now I can understand it.
Any number should be expressed as multiplication of prime factors, and through these I will get all numbers which divide evenly to the original number. or the original number is divisible by all these numbers !

Brent, your tip was also useful !
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