Question

What will be the remainder when 13^36 is divided by 2196?

Answer 1

1 will be the remainder

Answer 2

When we divide $13^{36}$ by 2196, the remainder will be equal to 1.

Given:

From the expression,

The divisor = 2196

The dividend = $13^{36}$

To Find:

The reminder

Solution:

It's fairly simple to find the answer to this question, as seen below.

We need to divide $13^{36}$ by 2196

That is,

$\frac{13^{36} }{2196}$

We know that,

$13^{36}$ can be written as,

$13^{36} = (13^{3})^{12}$

We have,

$13^{3} = 2197$

Therefore,

$13^{36} = (13^{3})^{12} = (2197)^{12}$

$(2197)^{12}$ can be written as $(2196 + 1)^{12}$

Now this resembles with $(a + b)^{2}$

We know that,

$(a + b)^{2} = a^{2} + b^{2} + 2ab$

So,

$(2196 + 1)^{12} = 2196^{12} + 1^{12} + 2$ × $2196$ × 1

When we divide $(2196 + 1)^{12}$ by 2196

Every terms of the equation will undergo division except $1^{12}$.

Hence, the reminder will be equal to 1.

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