Number System : How to find remainder when multiplication of Numbers is divided by a Number
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Lets try to find remainder when 16 x 21 is divided by 13.
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Steps :
- Write the digits as the number or multiple of number plus left amount for both the numbers.
- Then expand it
- Divide the expansion by divisor.
16 x 37
=
(13 + 3) x (13 x 2+ 11)
=
13 x 13 x 2 + 3 x 13 x 2 + 13 x 11 + 3 x 11
Dividing it by 13, we get remainder same as of 3 x 11/13 i.e. 7.
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So , remainder of a multiplication of a number when divided by a divisor, is same as the remainder of multiplication of remainders of each individual numbers divided by divisor.
Mathematically ,
R(A x B x C x D/P) = R[{R(A/P) x R(B/P) x R(C/P) x R(D/P)}/P], where R(A/P) denotes the remainder of A/P.
We denote the transition by ——-R———>
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Lets take an example .
Find the remainder of 189 x 1465 x 15678 x 156 when divided by 12.
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It looks very tough isn’t it. Lets make it easy by following steps which we learnt above.
(189 x 1465 x 15678 x 159 /12) — R–> (9 x 1 x 6 x 3 /12) = 27 x 6 /12 — R –> 3 x6 /12 = 18/12 –R–> 6
So Remainder is 6.
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In this way we can easily figure out the remainder of very big multiplication of numbers easily.
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