# What is the remainder of 3^29 divided by 4?

##### 2 Answers

Since 29 is an odd number,

the remainder happens to be 3

#### Explanation:

when 3^0 =1 is divided by 4, the remainder is 1

when 3^1 =3 is divided by 4, the remainder is 3

when 3^2 =9 is divided by 4, the remainder is 1

when 3^3 =27 is divided by 4, the remainder is 3

ie

all the even powers of 3 has remainder 1

all the odd powers of 3 has remainder 3

Since 29 is an odd number,

the remainder happens to be 3

3

#### Explanation:

If you look at the pattern of

etc.

You could make a conjecture that if the power is even, then the decimal part of the answer is equivalent to