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What is the remainder when the number 14^2*15^8 is divided by 5?
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Bunuel
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What is the remainder when the number 14^2*15^8 is divided by 5? [#permalink] New post  15 Jan 2017, 08:15
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What is the remainder when the number 14^2*15^8 is divided by 5?

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B. 1
C. 2
D. 4
E. 5
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OptimusPrepJanielle
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What is the remainder when the number 14^2*15^8 is divided by 5? [#permalink] New post  Updated on: 19 Jan 2017, 16:23
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Bunuel wrote:
What is the remainder when the number 14^2*15^8 is divided by 5?

A. 0
B. 1
C. 2
D. 4
E. 5


Last digit of 14^2 = 6
Last digit of 15^8 = 5

Last digit of multiplication = 0
Hence the remainder when (14^2)*(15^8) is divided by 5 = 0

Other way:
14^2*15^8 = 14^2*3^8*5^8
Hence this will always be divisible by 5

Correct option: A

Originally posted by OptimusPrepJanielle on 15 Jan 2017, 12:45.
Last edited by OptimusPrepJanielle on 19 Jan 2017, 16:23, edited 1 time in total.
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harucci
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What is the remainder when the number 14^2*15^8 is divided by 5? [#permalink] New post  15 Jan 2017, 15:33
This post is not written properly. Since parentheses are needed to illustrate the exact operations.
In the current way written (14^2*15^8) it means: 14^{2*15^{8}}

The OptimusPrepJanielle gave a solution for (14^2)*(15^8) and this is perfectly divided by 5, since 15 is divided perfectly by 3, hence the quotient is an integer and the remainder 0. Which requires 0 operations.

The author should clarify what the right notation is.
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nahid78
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Re: What is the remainder when the number 14^2*15^8 is divided by 5? [#permalink] New post  15 Jan 2017, 16:22
Bunuel wrote:
What is the remainder when the number 14^2*15^8 is divided by 5?

A. 0
B. 1
C. 2
D. 4
E. 5


No matter what 14^2 is, 15^8 will give a 5 at the end, which will be divisible by 5.
So ans is A.
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OptimusPrepJanielle
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Re: What is the remainder when the number 14^2*15^8 is divided by 5? [#permalink] New post  19 Jan 2017, 16:24
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harucci wrote:
This post is not written properly. Since parentheses are needed to illustrate the exact operations.
In the current way written (14^2*15^8) it means: 14^{2*15^{8}}

The OptimusPrepJanielle gave a solution for (14^2)*(15^8) and this is perfectly divided by 5, since 15 is divided perfectly by 3, hence the quotient is an integer and the remainder 0. Which requires 0 operations.

The author should clarify what the right notation is.

Hi harucci,

Thanks a lot for pointing this out, I have included the parenthesis in my original post.
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Re: What is the remainder when the number 14^2*15^8 is divided by 5? [#permalink]
19 Jan 2017, 16:24
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