200 Divided By 1 4

78.

What will be residuum when 17²⁰⁰ is divided by 18 ?

[A].	17
[B].	16
[C].	ane
[D].	ii

Answer: Option C

Explanation:

When n is even. (10 ⁿ - a ⁿ) is completely divisibly by (x + a)

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

(17²⁰⁰ - 1) is completely divisible by xviii.

On dividing 17²⁰⁰ by 18, we go 1 as residue.

Akhil said: (Nov thirteen, 2011)
Why cant information technology exist (17^200-ii^200) is completely divisible by 17+2=xix ?

Gururaj said: (Mar half-dozen, 2013)

Uncomplicated way way is:

17 ^2 %18 =one.

(17^2)*(7^100) %18 will as well exist 1.

Siddeswara Reddy said: (Jun 14, 2014)
When (10-1)^north is divided past X then R=i, If northward is fifty-fifty natural number and if n is odd natural number then R = X-1.

Swapnil said: (Jul 11, 2014)
How can nosotros write 17^200-1^200 this one is not equals to 17^200. Nosotros tin write eighteen as 17+1 just why nosotros take 17^200-1.

Anusha said: (Nov one, 2014)

(17*17*17*......*17) /18.

18-17 = i.

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

Ability is still, 1/18.

Respond is i (numerator).

Prasanna Kartik said: (Jul 8, 2015)

Hello guys,

Nosotros can solve information technology by negative reminders concept.

Here is our question 17^200 is divided past eighteen.

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

Instance xi/3 positive reminder equally we know is two and the negative reminder is -i(eleven-12).

Gaurav said: (Feb 28, 2016)
eleven/3 reminder is 2 merely what is -1(11-12)? Please explain more.

Bharath said: (Aug thirty, 2016)
17^200 = (eighteen - ane)^200 gives (18^200) - 2 * eighteen + one which give remainder i when divided by 18.

Mir Rokon Uddin said: (January ten, 2017)
Information technology is notable that the ability of 17 is even. So we can consider 17^2 and divide it by 18. And we got 1 equally a reminder. And then the answer is 1.

Dev said: (Mar 23, 2017)
Please give me solution for finding the value of R. And explicate the reply. 26^57÷29 = R. 128^100÷153 = R. ii^187÷51 = R. 17^14÷72 = R.

Sweety said: (May 28, 2017)
Delight, anyone explain this clearly.

ESRAK AHMED KAFI said: (Jun 2, 2017)
x^northward -1 is divisible past (X+1) when n is fifty-fifty. then, when we will split up 10^due north past (X+ane) the remainder will be definitely 1. Case: 2^2 =4, when 4 is divided by (two+1) i.east. iii, then the remainder volition be one.

Shubham said: (Jun 29, 2017)
Can somebody give all the partitioning rules for term (ten^n - a^n).

Bhavesh Sharma said: (Jul five, 2017)
I have more uncomplicated solution: 17^2 divided by 1 then the remainder is 1. Then we tin write 17^200 as( 17^2)^100. So nosotros get 1 remainder.

Manoranjan Sahoo said: (Jul 1, 2018)
(17^199+17)/18, (17^199+ane)/18 is completely divisible, and the reminder is sixteen.

Rounak said: (Aug nineteen, 2018)
What to do when n is odd number?

Gopi said: (Jan 25, 2019)

17^200 - 1 = 18 * quotient.
So,
17^200 = 18 * quotient + 1.

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

And then, ans = ane.

Praful Kumar said: (Mar 9, 2019)

@All.

Uncomplicated, it is solved by;

Rule1: If a^even no. ÷ a+1, then the remainder will always be ane.
Rule2: If a^odd no. ÷ a+1, then the remainder volition e'er be a.
Rule3: If a^n. ÷ a-1, then the remainder will always be 1, whether n is even or odd.

Hamsa said: (Oct 30, 2019)
What is the balance when 79^59 is divided by 40.

Sekhar said: (February xvi, 2020)
What is the residuum when 83^63 is divided by fourteen.

Ravikumar Chauhan said: (April 7, 2020)

But from where 1^200 come up?

17^200 is same or has the same value 17^200-1^200.

Please explain.

Lakshmi said: (May 29, 2020)
I don't understand, please explicate it.

Kaveri said: (Oct 5, 2020)
When 17^200 is completely divisible by 18 and so the remainder needs to exist 0 right, then how come ane?

Jigsa said: (April 3, 2021)
x^northward +1 is divisible by (X+ane) when due north is odd.

HRK said: (Sep 1, 2021)

@All.

the Elementary logic is;
18 = 9*2.

Given a number in the question is divisible past 2 as it will take 0 in the unit of measurement digit.
At present checking for 9, 17 = 1+7 = eight, but this is not divisible by 9.

To arrive divisible add 1 in the unit digit, i.due east. ane+7+1 (the number be similar 170000.....1)
And so this added number is the remainder.

Meezab E Rehmat said: (Dec 27, 2021)

@All.

Here, -1 ways ane is the balance.

And 18=17+1.