What would be the remainder when 3^37 is divided by 79?

Question

Please show the method.

Answer 1

First calculate what 3^37 is, which is:      450283905890997400

Next divide this number by 79, which is:   5699796277101233

This number goes evenly into this number. So there isn't a remainder.

If there was a remainder to be found it would be found like this:

First do the above steps.

Next see the whole number that you found after dividing the number by 79 (the number without the decimal)

Multiply this whole number by 79 (in this case)

Then subtract this number from the original number you got before dividing it.

This will give you your remainder, which should be less then your divisor.

I hope this helped!

Answer 2

3^4=81

81 divided by 79 remainder 2

3^37= (3^4)^9 *3

=( (79N+2)^9  )*3

if you expand it, everything with N will accompanied by 79.

So, we only need to worry about  2^9 *3

2^9 = 512

512 divided by 79 remainder 38

38*3 = 114   divided by 79 remainder  35

35 is the answer.

Answer 3

This is easily done with a calculator. Even with the one on your computer. Open it by clicking (on Windows) on Start>All Programs>Accessories>Calculator. Use the scientific mode by clicking on View>Scientific. Then simply do this:

3^37=450283905890997363

450283905890997363/79=5699796277101232...

Since the division is not exact, just take the whole part (before the decimal point) of the answer: 5699796277101232 and multiply it by 79 like this:

5699796277101232 x 79 = 450283905890997328

Now just substract this number to the original:

450283905890997363 - 450283905890997328 = 35

And there it is, the remainder of 3^37 / 79 is 35.

To check its true just do this:

5699796277101232 x 79 + 35 = 450283905890997363 = 3^37

To see how this method works here's an easier example:

35 divided by 4

35/4=8.75

8x4=32

35-32=3

8x4+3=35

So the remainder is 3.

Hope it helps.