What is the remainder when 7^442 is divided by 10?

Question

What is the remainder when  7^{442}  is divided by 10?

A. 1 
B. 3 
C. 5 
D. 7 
E. 9

LucienH · Answer

Using the cyclicity of powers, the powers of 7 will always have the following unit digits: 
7,9,3,1 
the power is 442, had it been 444 the unit digit would have been a 1 (since 444 is divisible by 4), therefore, the unit digit will be two steps before that, i.e. ---> 9

9/10 leaves a remainder of 9

Answer E

Amaraetike · Answer

Using cyclicity of power:
7^1 =7
7^2 = 9
7^3 = 3
7^4 = 1
7^5 = 7
(And the cycle continues)

442 is not divisible by 4, but 444 is divisible so at 7^4 the unit digit will be 1, since 444 is +2 greater than 442 (go back twice), 442 will be = 9

I hope this helps

Posted from my mobile device

BrushMyQuant · Answer

What is the remainder when  7^{442}  is divided by 10

Theory: Remainder of a number by 10 is same as the unit's digit of the number

( Watch this Video  to Learn  How to find Remainders of Numbers by 10 )

Using Above theory Remainder of  7^{442}  by 10 = unit's digit of  7^{442}

Now to find the unit's digit of  7^{442}  , we need to find the pattern / cycle of unit's digit of power of 7 and then generalizing it.

Unit's digit of  7^1  = 7
Unit's digit of  7^2  = 9
Unit's digit of  7^3  = 3
Unit's digit of  7^4  = 1
Unit's digit of  7^5  = 7

So, unit's digit of power of 7 repeats after every  4^{th}  number.
=> We need to divided 442 by 4 and check what is the remainder
=> 442 divided by 4 gives 2 remainder

=>  7^{442}  will have the same unit's digit as  7^2 
=> Unit's digits of  7^{442}  = 9

So,  Answer will be E 
Hope it helps!

MASTER How to Find Remainders with 2, 3, 5, 9, 10 and Binomial Theorem

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

What is the remainder when 7^442 is divided by 10?

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What is the remainder when 7^442 is divided by 10?

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