What is the remainder when 80^{35} is divided by 81?

By remainder theorem , when (a+b)^{N} divided by a, the remainder will be b^{N}.

80^{35} when divided by 81.

Or (81-1)^{35} when divided by 81.

Remainder will be (-1)^{35} or -1.

Hence remainder will be -1 + 81 = 80.

- A person distributes pens among his three friends A, B and C in the ratio 1/5 : 1/6: 1/8 . What is the minimum number of pens that the persons should have?
- A person hired a car for few days. The rent is charged @ Rs 100 per day for first 2 days, Rs 200 per day for next 7 days and Rs 387 per day thereafter. Registration fee is Rs 100 at the beginning. If the person has paid Rs. 4,409, for how many days did he hire the car?
- Find out the quantity of four-digit numbers that can be created by utilizing the digits from 1 to 9 if repetition of digits is not allowed?
- Find the Sum of all the even Factors of ‘240’
- If (3 - 4/(1+ 2/(3+ 1/(2+1/3))))th part of a journey takes 45 minutes, then to complete 4/5th of that journey, it will take:
- Find the smallest number which when successively divided by 4, 7 and 5 will give the remainder 2, 1, 3.
- The sides of a right angled triangle is 6, 8 and 10cm. Another triangle is formed by joining the mid points of all the sides of the triangle and in the same process infinite number of triangles is being formed, and then find the sum of areas of all such infinite number of triangles?
- How many Zeros can be formed by multiplying 10×20×30×40×…………….× 3000
- Least number which when multiplied to 245 gives a perfect square:
- Three fruit sellers P, Q and R have different quantities of fruits to sell. P and Q together have fifteen more than half of quantity what P and R together have. Q’s quantity is one-fifth of the double of R’s quantity. Also, P has one-third of what R has. Find the quantity that Q has.

More No. System Questions

×