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For which n is the remainder largest when the number 817,380 is divide

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Manager
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Joined: 26 Dec 2018
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For which n is the remainder largest when the number 817,380 is divide  [#permalink]

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New post 06 Jan 2019, 21:48
1
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A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

76% (01:18) correct 24% (01:19) wrong based on 34 sessions

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For which n is the remainder largest when the number 817,380 is divided by n?

A 4
B 5
C 6
D 8
E 9

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Manager
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Re: For which n is the remainder largest when the number 817,380 is divide  [#permalink]

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New post 07 Jan 2019, 00:54
1
Quick: The number is divisible by 5,6,9 (eliminate all)

Between 4 and 8, check is the number is divisible by 4 by prime factorization, you'll find its twice divisible by 2 which means yes, so 8 must be it.
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Re: For which n is the remainder largest when the number 817,380 is divide  [#permalink]

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New post 07 Jan 2019, 01:29
1
Hi,

Knowing the divisibility rules will help to solve this question faster.

A. Divisibility rule of 4 – Last two digits must be divisible by 4. So here last two digits is 80. So remainder is 0.

B. Divisibility rule of 5 – Last digit has to be 0 or 5. So again remainder is 0. So we can eliminate A and B options.

C. Divisibility rule of 6 – it has to be divisible by both 2 and 3. 817380 is an even number(last digit 0) and for divisibility of 3 – sum of the digits should be divisible by 3. 8+1+7+3+8+0 = 27 is divisible by 3. So remainder 0. Eliminate it.

D. Divisibility rule of 8 – last three digits has to be divisible by 8. Here 380 is not divisible, so its has a remainder greater than 0. No need to find the exact remainder.(Remainder is 4).

E. Divisibility rule of 9 – Sum of the digits should eb divisible by 9. 8+1+7+3+8+0 = 27 is divisible by 9. So remainder 0. Eliminate it.

So the answer is D.

Hope this helps.

Regards,
Junaid.
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Re: For which n is the remainder largest when the number 817,380 is divide   [#permalink] 07 Jan 2019, 01:29
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For which n is the remainder largest when the number 817,380 is divide

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