Question

if 67^99 is devided 7, what is the remainder ​

Answer 1

Answer:

Answer is 4.

EXPLAIN:-

1. It doesn't matter how much power is there on that particular number.
2. Now divide 67 by 7, you will find that remainder is 4.
3. Now if you multiple 67, 99 times then also remainder will be 4.

EXAMPLE:-

1. If you divide 4 by 3 remainder will be 1.

• Again divide 4^2 by 3 remainder will be 1.
• Again divide 4^3 by 3 remainder will be 1.
• it means that power doesn't matter remainder will be same for all if you divide it with same number.

Thank you.

Tushar Das

Answer 2

Answer:1

Step-by-step explanation:'someone mentioned that if number n leaves x remainder then for any power that number remainder will still be x.

remainder:

(4/3)=1  (16/3)=1 (64/3)=1

but its not always true.

Example: (8/3)= 2 (64/3)=1 (512/3)=2

they do follow some pattern like above example. it may or may not be same remainder.

answer of above question:

(67)=(63+4)

63 will be perfectly divisible with 7 so

taking only 4

4^99

checking for 4^1=4/7=4 remainder

4^2=16/7=2 remainder

4^3=64/7=1 remainder

4^4=256/7=4 remainder

it will follow the same pattern from now on.  (1,4,7,10,13...):4

(2,5,8...):2

(3,6,9...99):1

it implies for power ^99 remainder will be 1