What is the remainder when 7^52 is divided by 2402 ?

Question

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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lacktutor · Answer

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.

scorp17 · Answer

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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EgmatQuantExpert · Answer

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  = 2401

Thus, option A is the correct answer.

Correct Answer: Option A

BrushMyQuant · Answer

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

https://www.youtube.com/watch?v=h1HTEhmUb1w

violinix · Answer

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

bumpbot · Answer

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What is the remainder when 7^52 is divided by 2402 ?

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What is the remainder when 7^52 is divided by 2402 ?

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