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555-605 Level|   Exponents|   Remainders|      
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Bunuel
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What is the remainder when 7^52 is divided by 2402 ? 21 Feb 2020, 06:19
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

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35% (medium)

Question Stats:

75% (01:51) correct 25% (01:58) wrong based on 275 sessions

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What is the remainder when \(7^{52}\) is divided by 2402 ?

A. 2401
B. 2394
C. 2387
D. 2381
E. 2374


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A
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What is the remainder when 7^52 is divided by 2402 ? 21 Feb 2020, 06:37
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What is the remainder when \(7^{52}\) is divided by 2402 ?
\(7^{52}= 7^{2*26}=49^{2*13}= 2401^{13}\)

--> \((2402-1)^{13}= 2402^{13} -2402^{12}*1\)+...\(-1\)
When it is divided by \(2402\), The remainder will be \(2402-1 =2401.\)

The answer is A.
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What is the remainder when 7^52 is divided by 2402 ? 21 Feb 2020, 06:43
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7^4= 2401 = 2402-1
7^52 = (2401)^13= (2402-1)^13
When we expand every segment will contain 2402 except -1^13.
So only -1^13 will give us the remainder .
-1 remainder is equal to 2401
my ans : A

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What is the remainder when 7^52 is divided by 2402 ? 21 Feb 2020, 10:26
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Solution



To find
We need to determine
    • The remainder when \(7^{52}\) is divided by 2402

Approach and Working out
Rem[\(7^{52}/2402\)] = Rem[\((7^4)^{13}/2402\)] = Rem[\((2402 – 1)^{13}/2402\)] = Rem[\((-1)^{13}/2402\)] = Rem[-1/2402] = 2401

Thus, option A is the correct answer.

Correct Answer: Option A
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What is the remainder when 7^52 is divided by 2402 ? 06 Oct 2024, 05:56
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We need to find the the remainder when \(7^{52}\) is divided by 2402 ?

We will be solving the problem using Binomial Theorem

We need to break the number into two numbers such that one number is a big number and closer to 2402 and other number is a smaller number

Now, \(7^4\) = 2401 = 2402 - 1

=> \(7^{52}\) = \(7^{4*13}\) = \(7^{4^{13}}\) = \(2401^{13}\) = \((2402-1)^{13}\)

Now, if we use Binomial Theorem to expand this then all the terms except the last term will be a multiple of 2402
=> All terms except the last term will give remainder of 0 when divided by 2402
=> Problem is reduced to what is the remainder when the last term (i.e. 13C13 * 2402^0 * (-1)^13) is divided by 2402
=> Remainder of 1 * 1 * -1 is divided by 2402
=> Remainder of -1 divided by 2402 = -1 + 2402 = 2401

So, Answer will be A
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 7^52 is divided by 2402 ? 25 Oct 2024, 16:30
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To add to the previously posted approaches:

You can calculate \(49^2\) easily by expanding with the binomial theorem: \(49^2=(50-1)^2=50^2-2*50+1^2=2500-100+1=2401\)
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