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If you divide 7^131 by 5, which remainder do you get?

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Re: If you divide 7^131 by 5, which remainder do you get?  [#permalink]

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New post 08 Apr 2018, 06:00
1
whenever you come across a question like this :-- a number raised to higher power of integer divided by 2,3,4,5,6,7,8,9..
and asking for remainder...then, the question is actually asking for the unit digit of the numerator..

now,
3^4 has a unit digit of 1 => unit digit of 1 will repeat after every fourth power of 3.

6 to the power anything, always has a unit digit of 6

7^4 also has a unit digit of 1 => unit digit of 1 will repeat after every fourth power of 7

now, 151 = 148 + 3

7^148 * 7^3 = unit digit of 1 * unit digit of 3 = unit digit of 3..

any number divided by 5 gives remainder = unit digit of the number, when unit digit is less than 5

and (unit digit - 5) , when unit digit is greator than 5
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Re: If you divide 7^131 by 5, which remainder do you get?  [#permalink]

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New post 09 Apr 2018, 15:31
blackcrow wrote:
If you divide 7^131 by 5, which remainder do you get?

A. 0
B. 1
C. 2
D. 3
E. 4



To determine the remainder when 7^131 is divided by 5, we need only to divide the units digit of 7^131 by 5.

Let’s determine the units digit of 7^131:

When writing out the pattern of 7 raised to positive integer exponents, notice that we are concerned ONLY with the units digit of 7 raised to each power.

7^1 = 7

7^2 = 9

7^3 = 3

7^4 = 1

7^5 = 7

The pattern of the units digits of powers of 7 repeats every 4 exponents. The pattern is 7–9–3–1. In this pattern, we see that all positive exponents that are multiples of 4 will produce a 1 as its units digit. Thus:

7^132 has a units digit of 1 and so 7^131 has units digit of 3. So, the remainder of 3/5 = 3.

Answer: D
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Re: If you divide 7^131 by 5, which remainder do you get? &nbs [#permalink] 09 Apr 2018, 15:31

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