Aptitude - Numbers - Discussion

Discussion Forum : Numbers - General Questions (Q.No. 78)
78.
What will be remainder when 17200 is divided by 18 ?
17
16
1
2
Answer: Option
Explanation:

When n is even. (xn - an) is completely divisibly by (x + a)

(17200 - 1200) is completely divisible by (17 + 1), i.e., 18.

   (17200 - 1) is completely divisible by 18.

   On dividing 17200 by 18, we get 1 as remainder.

Discussion:
27 comments Page 1 of 3.

HRK said:   4 years ago
@All.

the Simple logic is;
18 = 9*2.

Given a number in the question is divisible by 2 as it will have 0 in the unit digit.
Now checking for 9, 17 = 1+7 = 8, but this is not divisible by 9.

To make it divisible add 1 in the unit digit, i.e. 1+7+1 (the number be like 170000.....1)
So this added number is the remainder.

Praful kumar said:   7 years ago
@All.

Simple, it is solved by;

Rule1: If a^even no. ÷ a+1, then the remainder will always be 1.
Rule2: If a^odd no. ÷ a+1, then the remainder will always be a.
Rule3: If a^n. ÷ a-1, then the remainder will always be 1, whether n is even or odd.
(1)

Prasanna Kartik said:   1 decade ago
Hi guys,

We can solve it by negative reminders concept.

Here is our question 17^200 is divided by 18.

17/18 negative reminder is -1. So (-1) ^200=1.

Example 11/3 positive reminder as we know is 2 and the negative reminder is -1(11-12).

ESRAK AHMED KAFI said:   9 years ago
x^n -1 is divisible by (X+1) when n is even. so, when we will divide X^n by (X+1) the remainder will be definitely 1.

Example: 2^2 =4, when 4 is divided by (2+1) i.e. 3, then the remainder will be 1.

Dev said:   9 years ago
Please give me solution for finding the value of R. And explain the answer.

26^57÷29 = R.
128^100÷153 = R.
2^187÷51 = R.
17^14÷72 = R.

Mir Rokon Uddin said:   9 years ago
It is notable that the power of 17 is even.

So we can consider 17^2 and divide it by 18. And we got 1 as a reminder. So the answer is 1.

Gopi said:   7 years ago
17^200 - 1 = 18 * quotient.
So,
17^200 = 18 * quotient + 1.

We have taken that 1 as a reminder in all type of problems.

So, ans = 1.

Bhavesh sharma said:   8 years ago
I have more simple solution:
17^2 divided by 1 then the remainder is 1.
So we can write 17^200 as( 17^2)^100.
So we get 1 remainder.

Swapnil said:   1 decade ago
How can we write 17^200-1^200 this one is not equals to 17^200.

We can write 18 as 17+1 but why we take 17^200-1.

Anusha said:   1 decade ago
(17*17*17*......*17) /18.

18-17 = 1.

(-1*-1*-1*.....*-1) /18.

Power is even so, 1/18.

Answer is 1 (numerator).


Post your comments here:

Your comments will be displayed after verification.