Question

What is the remainder when 17^23 is divided by 16?​

Answer 1

when 1723 is divided by 16, the remainder will be 1.

Aaahhh ! Let me explain you ..

In this section, you will learn how to find remainder when 17 power 23 is divided by 16.

Let us take exponents 0, 1, 2, 3, ....one by one for 17.

For example, if we take exponent 0 for 17, we get

170 = 1

Here, 1 is less than the divisor 16 and 1 can not be divided by 16.

If the dividend is less than the divisor, then the dividend itself has to be considered as 'Remainder'.

So, if 170 is divided by 16, the remainder is 1.

If the dividend is greater than the divisor, then we have to divide the dividend by the divisor and get remainder.

Let us deal our problem in this way. [ Look at the attached file ]

When we look at the (attached file) table carefully, 170 is divided by 16, the remainder is 1.

Again we get remainder 1 for the exponent 1.

Next we get remainder 1 for the exponent 2 and so on.

So, we get remainder 1, for all the exponents we take for 17.

Therefore, when 1723 is divided by 16, the remainder will be 1.

Answer 2

Answer:

The remainder is $1$ when $17^{23}$ is divided by $16$.

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 expression as follows:

$17^{23}$

To find:- The remainder when $17^{23}$ is divided by the number $16$.

When $17$ is divided by $16$. Then,

By divisional algorithm,

$17=1\times16+1$

Here, remainder is $1$.

Step 2 of 2

In modulo form,

$17$ ≡ $1\ (mod16)$

Taking raise to the power $23$ both the sides as follows:

⇒ $17^{23}$ ≡ $1^{23}\ (mod16)$ . . . . . (1)

Notice that,

$1^{23}=1$

From equation (1), we get

$17^{23}$ ≡ $1\ (mod16)$

Therefore, the remainder is $1$ when $17^{23}$ is divided by $16$.

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