Question

If X = 1537 x 1539 x 52201, find the remainder when X is divided by 17.​

Answer 1

Given: X = 1537 x 1539 x 52201

To Find: The remainder

Solution:

Here, X = 1537 x 1539 x 52201

(Solve the above equation using simple multiplication to find the value of X.)

X= 2365443*52201

   = 123478490043

Now, divide X=123478490043(dividend)  by 17 (divisor)

(In Maths, the division process is opposite of  multiplication process)

We get, quotient = 7263440590

and remainder = 13

Hence the remainder is 13 when X is divided by 17.

Answer 2

Given :- X = 1537 x 1539 x 52201

To Find :- The remainder when X is divided by 17 ?

Solution :-

Let us first take some examples :-

Example (1) :-

→ (20 * 18) ÷ 17

→ 360 ÷ 17

→ Remainder 3

now,

→ 20 ÷ 17 = Remainder 3

→ 18 ÷ 17 = Remainder 1

then,

→ (20 * 18) ÷ 17 = (3 * 1) ÷ 17 = 3 ÷ 17 = Remainder 3 .

Example (2) :-

→ (6 * 7 * 8 * 9) ÷ 5

→ 3024 ÷ 5

→ Remainder 4

now,

→ 6 ÷ 5 = Remainder 1

→ 7 ÷ 5 = Remainder 2

→ 8 ÷ 5 = Remainder 3

→ 9 ÷ 5 = Remainder 4

then,

→ (6 * 7 * 8 * 9) ÷ 5 = (1 * 2 * 3 * 4) ÷ 5 = 24 ÷ 5 = Remainder 4 .

Conclusion :- Product of any two or more numbers has the same remainder when divided by any natural number, as the corresponding product of their remainders .

In order to save time and long calculation , solving given problem with this concept now :-

→ (1537 x 1539 x 52201) ÷ 17 = Remainder ?

So,

→ 1537 ÷ 17 = Remainder 7

→ 1539 ÷ 17 = Remainder 9

→ 52201 ÷ 17 = Remainder 11

then,

→ (1537 x 1539 x 52201) ÷ 17

→ (7 × 9 × 11) ÷ 17

→ 693 ÷ 17

→ 13 (Ans.)

Hence we can conclude that, the remainder when X is divided by 17 is equal to 13 .

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