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A question about Math conventions on GRE

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A question about Math conventions on GRE [#permalink] New post 27 Jan 2019, 23:25
HI

Can someone please explain the highlighted part in the following?

If r, s, and t are integers and then rs = t, r and s are factors, or divisors, of t; also, t is a multiple of r (and of s) and t is divisible by r (and by s). The factors of an integer include positive and negative integers. For example, −7 is a factor of 35, 8 is a factor of -40 and the integer 4 has six factors: -4,-2,-1,1, 2, and 4. The terms factor, divisor, and divisible are used only when r, s, and t are integers. However, the term multiple can be used with any real numbers s and t provided r is an integer. For example, 1.2 is a multiple of 0.4, and is a −2π is a multiple of π.



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Re: A question about Math conventions on GRE [#permalink] New post 05 Feb 2019, 13:21
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Hey there!

What you need to know here are that the terms "factor," "divisor," and "divisible" only apply to integers. Otherwise, there would be an infinite number of factors for every number.

So, 10 is a factor of 100, because 10(10) = 100. Everything is an integer. 100 is divisible by 10, and 10 is a divisor of 100.

However, 8 is not a factor of 100, even though 8(12.5) = 100. In that case, 12.5 is not an integer, so that throws everything off. When we're talking about factors, divisible, and divisors, everything must be an integer.

9.2, then, is not divisible by anything, and is not a factor of anything, and does not have any divisors.

However, 9.2 is a multiple of 4.6. This is because 2(4.6) = 9.2. This means that the term multiple is a bit more flexible. It can be applied to non-integers so long as one of the numbers being multiplied is an integer.

The number 4.84 is not a multiple of 2.2, because 2.2(2.2) = 4.84. Neither of the numbers being multiplied are integers, so 4.84 is not a multiple.

But 4.4 is a multiple of 2.2, because 2(2.2) = 4.4. Since one of the numbers being multiplied is an integer, 4.4 is a multiple of the other one.

Does that make sense?
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Re: A question about Math conventions on GRE [#permalink] New post 05 Feb 2019, 22:56
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fifan wrote:
HI

Can someone please explain the highlighted part in the following?

If r, s, and t are integers and then rs = t, r and s are factors, or divisors, of t; also, t is a multiple of r (and of s) and t is divisible by r (and by s). The factors of an integer include positive and negative integers. For example, −7 is a factor of 35, 8 is a factor of -40 and the integer 4 has six factors: -4,-2,-1,1, 2, and 4. The terms factor, divisor, and divisible are used only when r, s, and t are integers. However, the term multiple can be used with any real numbers s and t provided r is an integer. For example, 1.2 is a multiple of 0.4, and is a −2π is a multiple of π.

Thanks



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Re: A question about Math conventions on GRE [#permalink] New post 16 Feb 2019, 18:19
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Referring one non-integer number a multiple of another non-integer number is not commonly accepted. In the literature, one may frequently encounter the phrase "integer multiple" or if what is meant is clear from the context, you may see an expression like "multiples of π" (for instance, if you are talking about values of x that satisfy the equation cos y = cos (x + y) for every y); however, I haven't come across any text where numbers such as 4.4, 6.6, 8.8 etc. are referred to as "multiples of 2.2" instead of "integer multiples of 2.2". The reason for this is simple: once your set is large enough to contain rational numbers, any number becomes a multiple of any other number. For instance, 2 is a multiple of 3 (because 3 x 2/3 = 2) and 3 is a multiple of 2 (because 2 x 3/2 = 3). When every number is a multiple of every other number, it makes no sense to use that phrase.
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Re: A question about Math conventions on GRE   [#permalink] 16 Feb 2019, 18:19
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