Question

Last two digit of 3^723 is
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Answer 1

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the last two digits of 3^723. is.

4.72236648286E21

Answer 2

Given:

Consider the given number is 3^723

Find:

Last two digit

Solution:

we know that if we apply modulo 100 over the given number we get last two digit

Therefore

3^723 (mod 100)

Here gcd(3, 100) = 1 therefore by Euler theorem

$3^{\phi (100)}\equiv 1(mod 100)$

$3^{40}\equiv 1(mod 100)$

Therefore

$3^{723}(mod 100)\equiv3^{720}.3^3(mod 100)$

$3^{723}(mod 100)\equiv(3^{4})^{180}.3^3(mod 100)$

$3^{723}(mod 100)\equiv1.3^3(mod100)$

$3^{723}(mod 100)\equiv27(mod100)$

Therefore the last two digit is 27.