Question

check whether (2016)^2019×(2015)^2020 can end with the digit '0'​

Answer 1

Answer:

Yes, the number ends with 0

Step-by-step explanation:

To make a 10 (for 0 to come in units place), we need a 2 and a 5.

In 2016, we can obtain a 2 and in 2015, we can get a 5.

Here, a 5 is extra. But that does not affect the answer. Because any number xyz0 * 5 = abc0 (the number can still end with zero)

Answer 2

For every natural numbers in the form $\displaystyle\sf{10n+6}$ for any whole number n,

$\displaystyle\longrightarrow\sf{(10n+6)^k\equiv6\pmod{10}}$

And for every natural numbers in the form $\displaystyle\sf{10n+5}$ for any whole number n,

$\displaystyle\longrightarrow\sf{(10n+5)^k\equiv5\pmod{10}}$

where k is a positive integer.

Therefore,

$\displaystyle\longrightarrow\sf{(2016)^{2019}\equiv6\pmod{10}}$

And,

$\displaystyle\longrightarrow\sf{(2015)^{2020}\equiv5\pmod{10}}$

Finally,

$\displaystyle\longrightarrow\sf{(2016)^{2019}\times(2015)^{2020}\equiv6\times5=30}\equiv\bf{0}\pmod{\sf{10}}$

Hence the statement is true that $\displaystyle\sf{(2016)^{2019}\times(2015)^{2020}}$ ends with the digit 0.