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Sub 505 (Easy)|   Exponents|   Remainders|      
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What is the remainder when 10^8 is divided by 11? 24 Nov 2023, 00:45
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B
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93% (00:55) correct 7% (01:06) wrong based on 182 sessions

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What is the remainder when 10^8 is divided by 11?

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B
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What is the remainder when 10^8 is divided by 11? 26 Nov 2023, 04:27
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For any power of 10 more than 1, the remainder will be 1 when divided by 11.
Thus, answer is B.

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What is the remainder when 10^8 is divided by 11? 26 Nov 2023, 10:39
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Reminder when 10^1 is divided by 11 = 10
Reminder when 10^2 is divided by 11 = 1 (because 11*9=99)
Reminder when 10^3 is divided by 11 = 10 (because 11*90=990)
Reminder when 10^4 is divided by 11 = 1 (because 11*909=9999)

From this pattern, we can deduce that reminder when 10^8 is divided by 11 will be 1.

Confirming our answer:
Reminder when 10^5 is divided by 11 = 10 (because 11*9090=99990)
Reminder when 10^6 is divided by 11 = 1 (because 11*90909=999999)
Reminder when 10^7 is divided by 11 = 10 (because 11*909090=9999990)
Reminder when 10^8 is divided by 11 = 1 (because 11*9090909=99999999)
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What is the remainder when 10^8 is divided by 11? 03 Oct 2024, 08:08
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We need to find the the remainder when \(10^{8}\) is divided by 11 ?

Let's solve the problem using two Methods:

Method 1: Cyclicity of Remainder of power of 10 by 11

To solve this problem we need to find the cycle of remainder of power of 10 when divided by 11

Remainder of \(10^1\) (=10) by 11 = 1
Remainder of \(10^2\) (=100) by 11 = 1
Remainder of \(10^3\) (=1000) by 11 = 1

=> Cycle is 1

=> Remainder of \(10^{8}\) by 11 = 1

Method 2: Binomial Theorem

\(10^{8}\) = \((11 - 1)^{8}\)

Remainder of \(10^{8}\) by 11 = Remainder of \((11 - 1)^{8}\) by 11

Now, if we use Binomial Theorem to expand this then all the terms except the last term will be a multiple of 11
=> All terms except the last term will give remainder of 0 when divided by 11
=> Problem is reduced to what is the remainder when the last term (i.e. 11C11 * 11^0 * (-1)^8) is divided by 11
=> Remainder of 1 * 1 * 1 is divided by 11
=> Remainder of 1 divided by 11 = 1
=> Remainder of \(10^{8}\) by 11 = 1

So, Answer will be B
Hope it Helps!

Watch following video to MASTER Remainders by 2, 3, 5, 9, 10 and Binomial Theorem

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What is the remainder when 10^8 is divided by 11? 04 Oct 2024, 02:17
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BrushMyQuant
We need to find the the remainder when \(10^{8}\) is divided by 11 ?

Let's solve the problem using two Methods:

Method 1: Cyclicity of Remainder of power of 10 by 11

To solve this problem we need to find the cycle of remainder of power of 10 when divided by 11

Remainder of \(10^1\) (=10) by 11 = 1
Remainder of \(10^2\) (=100) by 11 = 1
Remainder of \(10^3\) (=1000) by 11 = 1

=> Cycle is 1

=> Remainder of \(10^{8}\) by 11 = 1

Method 2: Binomial Theorem

\(10^{8}\) = \((11 - 1)^{8}\)

Remainder of \(10^{8}\) by 11 = Remainder of \((11 - 1)^{8}\) by 11

Now, if we use Binomial Theorem to expand this then all the terms except the last term will be a multiple of 11
=> All terms except the last term will give remainder of 0 when divided by 11
=> Problem is reduced to what is the remainder when the last term (i.e. 11C11 * 11^0 * (-1)^8) is divided by 11
=> Remainder of 1 * 1 * 1 is divided by 11
=> Remainder of 1 divided by 11 = 1
=> Remainder of \(10^{8}\) by 11 = 1

So, Answer will be B
Hope it Helps!

Watch following video to MASTER Remainders by 2, 3, 5, 9, 10 and Binomial Theorem

Show more
Method 3: Look at the answer choices
Self explanatory;)
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