Latest self Aptitude Question SOLUTION: what is the remainder when 7^700 is divided by 100?

• Placement Papers
• /
• self
• /
• Numerical Ability
• /
• Number System

self Question Papers:

(#M40013502) SELF Numerical Ability question Keep an EYE

what is the remainder when 7^700 is divided by 100?

Pranita Sharma (11 years ago)

Solved sanjana Read Solution (10)

Is this Puzzle helpful?   (35)   (16) Submit Your Solution Number System

Read Solution (10) :

sanjana  (11 years ago)

ans will be 1..
as when 7^1 is divided by 100,denremainder ll be 7..wen 7^2 is divided by 100,den rem-49..wen 7^3--rem will be 43..wen 7^4 --rem will be 1..wen 7^5--rem will be 7..wen 7^6--rem will be 49..if u ll go on checking like the other powers..u ll find after 7^4 its repeating...ques is to find out 7^100..so of u ll take the ramainder as a pair of 4(7,49,43,1)..den u cn get remainder will be 1 for 100

Is this solution Helpfull? Yes (15) | No (1)  

SDeep Bhattacharya  (11 years ago)

(7^700)mod100= [7^(2*350)]mod100=[49^350]mod100=[(50-1)^350]mod100=[{350C349}*50*(-1)^349 +350C350*(-1)^350]mod100 = [-350*50+1]mod100=1mod100
So, evidently, the remainder will be 1.

Is this solution Helpfull? Yes (6) | No   

Rakesh Kumar Kohli  (11 years ago)

7^700 = (7^4)^ 175 = (2401)^175
this number has last two digits 01. So when divided by 100, it will give reminder as 1.

Is this solution Helpfull? Yes (4) | No   

teja  (11 years ago)

49..7^1/100=7
7^2/100=49
7^3/100=43
7^4/100=1
cycle repeats..so 700/4=2
49

Is this solution Helpfull? Yes (3) | No   

saleem sarfani  (11 years ago)

43.
7^0/100=1
7^1/100=7
7^2/100=49
7^3/100=43
..
7^7/100=43..
similarly.....
7^7/100=43

Is this solution Helpfull? Yes (3) | No (2)  

akshya dhingra  (11 years ago)

7^4/100 will give 1 remainder...so 700/4=0.
so remainder will be=1.

Is this solution Helpfull? Yes (1) | No   

Pranita Sharma  (11 years ago)

@teja .. your solution is helpful , but got stuck up at the end.. how can I be sure that 700 is in that position? You've given 700/4=2. how can it be when 700/4=175.

Is this solution Helpfull? Yes | No (1)  

teja  (11 years ago)

yes..i was mistaken at the end..may b remainder is 1

Is this solution Helpfull? Yes | No   

Pranita Sharma  (11 years ago)

still confused..

Is this solution Helpfull? Yes | No (1)  

Anuj Katiyal  (11 years ago)

any methods to solve these remainder type questions ??

Is this solution Helpfull? Yes | No (1)  

Please Login to Read Solution.