Find the remainder!

Number Theory Level 2

Whats the remainder when − 22 -22 is divided by 7?


The answer is 6.

Ayushman Chahar by Ayushman Chahar , 21, India

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2 solutions

DarkMind S.
Mar 31, 2017

-22 = -7(3) - 1

We want the form N = DQ + R

Now, a remainder cannot be negative. So we write. "" -1"" as -7 + 6. Then we have :

-22 = -7(3) - 7 + 6

-22 = -7 [ (3) + 1 ] + 6

Done

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Denton Young
Dec 26, 2015

Sure. Since 28 is an exact multiple of 7, the remainder when -22 is divided by 7 is the same as when (-22 + 28) is divided by 7. -22 + 28 is equal to 6. the remainder when 6 is divided by 7 is 6.

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Moderator note:

Simple standard approach. Remember that by definition, the remainder r r when divided by d d satisfies 0 ≤ r \< d 0 \leq r \< d .

Could you please elaborate it more.

Ayushman Chahar - 5 years, 5 months ago

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Sure. Since 28 is an exact multiple of 7, the remainder when -22 is divided by 7 is the same as when (-22 + 28) is divided by 7. -22 + 28 is equal to 6. the remainder when 6 is divided by 7 is 6.

Denton Young - 5 years, 5 months ago

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