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Which of the following numbers does not have a factor (other than 1)

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Sajjad1994
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Which of the following numbers does not have a factor (other than 1) [#permalink] New post   22 Oct 2020, 03:24
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61% (01:46) correct 39% (01:26) wrong based on 44 sessions
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Which of the following numbers does not have a factor (other than 1) which is a perfect square?

(A) 48

(B) 117

(C) 245

(D) 297

(E) 345
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E
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Re: Which of the following numbers does not have a factor (other than 1) [#permalink] New post   22 Oct 2020, 07:10
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48 is divisible by 4, and 117 and 297 are divisible by 9 (as we can see by summing their digits). Since 250 = 5*50, then 245 = 5*49, so 245 is divisible by 7^2. So the answer is 345, which is equal to 5*69 = 5*3*23, and thus has no square divisor greater than 1.
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Re: Which of the following numbers does not have a factor (other than 1) [#permalink] New post   22 Oct 2020, 11:27
Which of the following numbers does not have a factor (other than 1) which is a perfect square?

(A) 48=4^2*4

(B) 117=3^2*13

(C) 245=7^2*5

(D) 297=3^2*33

(E) 345=3*5*23
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Re: Which of the following numbers does not have a factor (other than 1) [#permalink] New post   22 Oct 2020, 15:51
A) 48

4^2*4

(B) 117

3^2*13

(C) 245

7^2*5

(D) 297

3^2*33

(E) 345

3*5*23
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Re: Which of the following numbers does not have a factor (other than 1) [#permalink] New post   27 Oct 2020, 09:23
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Sajjad1994 wrote:
Which of the following numbers does not have a factor (other than 1) which is a perfect square?

(A) 48

(B) 117

(C) 245

(D) 297

(E) 345

Solution:

We can check each given answer choice:

A) 48 = 4 x 12

B) 117 = 9 x 13

C) 245 = 49 x 5

D) 297 = 9 x 33

E) 345 = 3 x 5 x 23

Answer: E
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Re: Which of the following numbers does not have a factor (other than 1) [#permalink] New post   27 Oct 2020, 10:40
IMO E

The answer choices seem to be small....just check with first few perfect squares say 4, 9, 16, 25, 36, 49

A. 48 - divisible by 4
B. 117 - divisible by 9
C. 245 - divisible by 49
D. 297 - divisible by 9. (Divisibility Rule of 9 - Sum of digits should be a multiple of 9)
E. 345 - (left Over and should be the answer, no need to check)
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Re: Which of the following numbers does not have a factor (other than 1) [#permalink]
27 Oct 2020, 10:40
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