Latest TCS Aptitude Question SOLUTION: 6^17+17^6 when divided by 7. What is the remainder?

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6^17+17^6 when divided by 7. What is the remainder?

Asked In TCS Akusumakar (11 years ago)

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Atul  (11 years ago)

6^17mod7....>(7-1)^17mod7=(-1)^17(because 7^17 is divisible by 7 ,



(-1)^17 mod 7=-1 .........(1)
17^6....>(7*2+3)^6 mod7=(3)^6 mod 7....729 mod 7=1 .......(2)
so now remainder when 6^17 + 17^6 is divided by 7
now eq (1)+(2) mod 7
(6^17 + 17^6)mod 7=(-1+1) mod 7=0 mod 7=0

0 remainder

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Sandeep singh  (11 years ago)

sorry by mistake

6^17+17^6
(6^16)*6 + (3)^6 when 17 divided by 7 remaindr is 3
(36^8)*6 + 27^2 when 36 and 27 divided by 7 remaindr is 1 and 6 respectively
(1^8)*6 + 6^2
6 + 36=42
divided by 7 we get 0 remaind

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arjun yadav  (11 years ago)

0
is the answer

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Brij  (11 years ago)

Remainder is zero when 6^17+17^6 is divided by 7.

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Sandeep singh  (11 years ago)

6^17+17^6
(6^16)*6 + (3)^6 when 17 divided by 7 remaindr is 3
(36^8)*6 + 27^2 when 36 and 27 divided by 7 remaindr is 1 and 6 respectively
(1^8)*6 + 6^2
6 + 36=42
divided by 7 we get 1 remaindr

Is this solution Helpfull? Yes (1) | No (11)  

sainath vanakuri  (11 years ago)

0 is the ans.
because 6^17 leaves "6" as remainder and 17^6 leaves 1. sum of the remainders is 7 and 7%7=0

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Ankush  (11 years ago)

6^17+17^6/7
for find the reminder..firstly
6^17/7+17^6/7
then..solve this..power term 17,6 is divided by 6 & without power term 6,17 is divided by 7..then reminder is..
6^5/7+3^0/7
then...7776/7+1/7..solve this..then
6+1/7..& answer is reminder 0....

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Akshay Jain  (11 years ago)

ans is 0
....
bcz 6^17 divided by 7 remender is 6
then 17^6 divided by 7 remender is 1
then 6+1 divided by 7 then remender is 0

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geetha  (11 years ago)

remainder:0

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jeyamurugan  (11 years ago)

answer is 0.

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pradeep  (11 years ago)

6^17+17^6
(6^2)^8*6+(14+3)^6
(1)^8*6+3^6
6+(3^2)^3
6+2^3
6+1
7
so remainder is 0;

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geetha  (11 years ago)

@atul can this method is applicable to any such questions? or only when divided by 7?

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vipin jain  (11 years ago)

6^17=((6^2)^8)*6= (1^8)*6=6........... 1 is reminder
17^6= 3^6.................. 3 is reminder
= 9^3= 2^3=8...........
6+8=14
14%2=0
so ans is 0

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