Is Zero to be considered a multiple of all the numbers?

g_beatthegmat

Hello,

Is Zero considered a multiple of all the numbers? I came across question # 13 in the Full-Length Practice Test of Kaplan which says-

beny · Posted: Thu Aug 02, 2007 5:43 pm Post subject:

0 is not considered a multiple of all numbers.

Either way, as you stated, with statement 2, the answer could be 7, 12, 17, 22, ... therefore, B is insufficient byitself.

I think the answer should be C, which would narrow the answer to 7 (since 12 is not a prime).

lalitgmat · Posted: Thu Aug 02, 2007 8:26 pm Post subject:

In this case also, only prime multiple of 5 and less than 15 is 5 itself only.
Hence, both statements ensure we have unique answer.

g_beatthegmat · Posted: Thu Aug 02, 2007 11:36 pm Post subject:

thanks benny and lalitgmat!

So the conclusion: Zero is NOT to be considered a factor of numbers. We can then define factor as:
Factor is a +ve number that completely divides into another +ve integer.

Thanks.

ash g · Posted: Fri Mar 07, 2008 7:03 pm Post subject:

Guys,
Just wanted to reopen this old thread. Is what is concluded in this thread correct ?
So the conclusion: Zero is NOT to be considered a factor of numbers.
This would also mean Kaplan explanation is incorrect which I dont think so.

I happen to believe that - All numbers divide zero and hence zero is a multiple of all numbers.

The example of LCM used to contradict above I think is incorrect.
The wiki definition of LCM is:
In arithmetic and number theory, the least common multiple or lowest common multiple (lcm) or smallest common multiple of two integers a and b is the smallest positive integer that is a multiple of both a and b. Since it is a multiple, it can be divided by a and b without a remainder. If there is no such positive integer, e.g., if a = 0 or b = 0, then lcm(a, b) is defined to be zero.

Any thoughts ??

Stuart Kovinsky · Posted: Sat Mar 08, 2008 7:01 am Post subject:

0 is a multiple of all numbers; 0 is a factor of no number.

Negative numbers are also multiples. For example, the set of all multiples of 5 is:

{..., -15, -10, -5, 0, 5, 10, 15, ...}

However, when we talk about the lowest common multiple, we're always referring to the smallest positive multiple of the numbers involved.

So, to review this particular question:

If x is prime, what's the value of x?

(1) x < 15

x could be 2, 3, 5, 7, 11, 13: insufficient

(2) (x - 2) is a multiple of 5

x could be billions and billions of different numbers: insufficient

Together:

If we look at our list from statement (1), (2-2)=0 which IS a multiple of 5 and (7-2)=5 which is ALSO a multiple of 5. Hence, x could still be either 2 or 7: choose (e).