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# The product of three distinct integers, a, b, and c, is 252. If each

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Math Expert
Joined: 02 Sep 2009
Posts: 58442
The product of three distinct integers, a, b, and c, is 252. If each  [#permalink]

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12 Dec 2016, 12:32
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The product of three distinct integers, a, b, and c, is 252. If each of the integers is greater than 1, what is the greatest possible value of the any of the three integers?

A. 126
B. 84
C. 63
D. 42
E. 28

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Posts: 359
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Re: The product of three distinct integers, a, b, and c, is 252. If each  [#permalink]

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12 Dec 2016, 14:05
1
Let’s maximize one of the integers a, b ,c. They should be positive, greater than 1 and distinct.

$$252 = 2^2*3^2*7$$

We’ll choose min values for a and b as 2 and 3 and all rest factors will go to c.

$$2*3*42$$

Using same procedure we can maximize a and b.

I hope I'm not too drowsy
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Joined: 07 Dec 2014
Posts: 1222
The product of three distinct integers, a, b, and c, is 252. If each  [#permalink]

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Updated on: 01 Feb 2019, 13:03
Bunuel wrote:
The product of three distinct integers, a, b, and c, is 252. If each of the integers is greater than 1, what is the greatest possible value of the any of the three integers?

A. 126
B. 84
C. 63
D. 42
E. 28

2 and 3 are the least possible two factors of 252
252/(2*3)=greatest possible third factor of 252=42
D

Originally posted by gracie on 12 Dec 2016, 15:19.
Last edited by gracie on 01 Feb 2019, 13:03, edited 1 time in total.
VP
Joined: 23 Feb 2015
Posts: 1257
The product of three distinct integers, a, b, and c, is 252. If each  [#permalink]

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12 Dec 2016, 17:30
Bunuel wrote:
The product of three distinct integers, a, b, and c, is 252. If each of the integers is greater than 1, what is the greatest possible value of the any of the three integers?

A. 126
B. 84
C. 63
D. 42
E. 28

The question says that abc=252
As the integer is greater than 1, we can surely take the first integer as 2,which is the lowest one. To find out the greatest possible value i have to choose or find out as lowest as possible. 252 is even so i can take the 2 as the lowest value. So, the remaining value will be 126. Now i have to find out the second lowest possible value from 126. I can not take it as 2 because the integer must be distinctive to each other. So, i can take it as 3 because 3 is the factor of 126 (the summation of 126 separately is 9, which is divisible by 3), so the highest possible value is exactly 42, which is D.
Thank you...

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Re: The product of three distinct integers, a, b, and c, is 252. If each  [#permalink]

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01 Feb 2019, 10:43
Bunuel wrote:
The product of three distinct integers, a, b, and c, is 252. If each of the integers is greater than 1, what is the greatest possible value of the any of the three integers?

A. 126
B. 84
C. 63
D. 42
E. 28

So 252 can be written as out of which the greatest possible value of the any of the three integers will be 42 * 3 * 2
2|252
2|126
3|63
3|21
7|7
|1

D
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Re: The product of three distinct integers, a, b, and c, is 252. If each   [#permalink] 01 Feb 2019, 10:43
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