Question

What is the remainder when 3^(40) is divided by 80?​

Answer 1

Answer:

$3 ^{40} mod80 = 48 \\ reminder = 48$

Step-by-step explanation:

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Answer 2

Answer:

The remainder is $1$ when $3^{40$ is divided by $80$.

Step-by-step explanation:

Recall the modulo identity,

If $a$ ≡ $b\ (modn)$ then $a^c$ ≡ $b^c\ (modn)$, where $c$ is any positive integer.

Step 1 of 2

Consider the given number as follows:

$3^{40}$

To find:- The remainder when $3^{40}$ is divided by the number $80$.

Notice that,

$3^4=81$

Apply divisional algorithm to the number $81$,

$81=1\times80+1$

Here, remainder is $1$.

Step 2 of 2

In modulo form,

$81$ ≡ $1\ (mod 80)$

or,

$3^4$ ≡ $1\ (mod 80)$

Taking raise to the power $10$ both the sides as follows:

⇒ $(3^4)^{10}$ ≡ $1^{10}\ (mod 80)$ . . . . (1)

Clearly, the value of $1^{10}=1$.

From (1), we get

$3^{40$ ≡ $1\ (mod 80)$

Final answer: The remainder is $1$ when $3^{40$ is divided by $80$.

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