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If r = 2^3 * 5^2 * 7 and s = 2^2 * 3^2 * 5, which of the

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If r = 2^3 * 5^2 * 7 and s = 2^2 * 3^2 * 5, which of the [#permalink]

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If r = 2^3 * 5^2 * 7 and s = 2^2 * 3^2 * 5, which of the following is equal to the greatest common divisor of r and s?

A. 2 * 5
B. 2^2 * 5
C. 2^3 * 5^2
D. 2*3*5*7
E. 2^3 * 3^2 *5^2 * 7
[Reveal] Spoiler: OA
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Re: If r = 2^3 * 5^2 * 7 and s = 2^2 * 3^2 * 5, which of the [#permalink]

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New post 18 May 2012, 17:42
GCD = product of prime factors raised to the least power =2^2 x 5

Option B
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Re: If r = 2^3 * 5^2 * 7 and s = 2^2 * 3^2 * 5, which of the [#permalink]

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New post 18 May 2012, 17:45
jsphcal wrote:
If r = 2^3 * 5^2 * 7 and s = 2^2 * 3^2 * 5, which of the following is equal to the greatest common divisor of r and s?

A. 2 * 5
B. 2^2 * 5
C. 2^3 * 5^2
D. 2*3*5*7
E. 2^3 * 3^2 *5^2 * 7


To find the greatest common divisor of two positive integers multiply the common factors of these integers by picking the lowest power of the common factors.

So, the GCD of r=2^3*5^2*7 and s=2^2*3^2*5 is 2^2*5.

Answer: B.
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Re: If r = 2^3 * 5^2 * 7 and s = 2^2 * 3^2 * 5, which of the [#permalink]

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Re: If r = 2^3 * 5^2 * 7 and s = 2^2 * 3^2 * 5, which of the [#permalink]

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New post 29 Nov 2016, 04:32
B) 2^2*5

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Re: If r = 2^3 * 5^2 * 7 and s = 2^2 * 3^2 * 5, which of the [#permalink]

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New post 29 Nov 2016, 09:29
jsphcal wrote:
If \(r = 2^3 * 5^2 * 7\) and \(s = 2^2 * 3^2 * 5\), which of the following is equal to the greatest common divisor of r and s?

A. 2 * 5
B. 2^2 * 5
C. 2^3 * 5^2
D. 2*3*5*7
E. 2^3 * 3^2 *5^2 * 7


GCD of \(r = 2^3 * 5^2 * 7\) and \(s = 2^2 * 3^2 * 5\) \(= 2^2*5\)

Hence, answer will be straight , (B) \(2^2 * 5\)
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Re: If r = 2^3 * 5^2 * 7 and s = 2^2 * 3^2 * 5, which of the [#permalink]

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New post 02 Dec 2016, 10:32
jsphcal wrote:
If r = 2^3 * 5^2 * 7 and s = 2^2 * 3^2 * 5, which of the following is equal to the greatest common divisor of r and s?

A. 2 * 5
B. 2^2 * 5
C. 2^3 * 5^2
D. 2*3*5*7
E. 2^3 * 3^2 *5^2 * 7


To determine the greatest common divisor (or greatest common factor) of any two numbers, we multiply together common prime factors with the smaller exponent. We are given the following:

r = 2^3 * 5^2 * 7

AND

s = 2^2 * 3^2 * 5^1

As we can see, 2 and 5 are the common prime factors. For the prime factor 2, the smaller exponent is 2 and for 5, the smaller exponent is 1. Thus, the GCF of r and s is 2^2 x 5^1.

Answer: B
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Re: If r = 2^3 * 5^2 * 7 and s = 2^2 * 3^2 * 5, which of the   [#permalink] 02 Dec 2016, 10:32
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