# Number System : How to find remainder when multiplication of Numbers is divided by a Number

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**Quotlly**

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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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