Question

The remainder obtained when 5^124 is divided by 124

Answer 1

The remainder will be 1.

Let's take 5^3 = 125

125/124 = 1 with remainder of 1

Any exponent of 5 greater than 3 will have the same remainder when divided by 124.

Answer 2

Answer:

The remainder is obtained 5 when 5^124 is divided by 124.

Step-by-step explanation:

We have,

${5}^{124}$$= { {5}^{3} }^{41} \times 5$

Now,

${5}^{3} = 1 \:( mod \: 124)$

${ ({5}^{3} )}^{41} = 1 \: (mod \: 124)$

${ {5}^{3} }^{41} .5 = 1.5 \:( mod \: 124)$

${5}^{124} = 5 \: (mod \: 124)$

The remainder is obtained 5 when 5^124 is divided by 124.

Here applied formulas are ${x}^{y} \times {x}^{z} = {x}^{y + z}$

and ${ ({x}^{y}) }^{z} = {x}^{y \times z} = {x}^{yz}$

Some others formula of power of indices,

${x}^{ - y} = \frac{1}{ {x}^{y} }$

${x}^{0} = 1$

${x}^{1} = x$

$\frac{ {x}^{y} }{ {x}^{z} } = {x}^{y - z}$

${y}^{z} \times {x}^{z} = {(yx)}^{z}$