Question

Last two digits of ${21}^{100}$ are

• A. $00$
• B. $01$
• C. $11$
• D. $21$

Answer 1

The correct option is B $01$

The last two digits follow a pattern

Number Last two digits

$21$ $21$

${21}^2$ $41$

${21}^3$ $61$

${21}^4$ $81$

${21}^5$ $01$

${21}^6$ $21$

${21}^7$ $41$

and so on.

The last digit is always 1, and the second to last goes through the sequence

$2,4,6,8,0,2,4,6,8,\mathrm{0....}$

So every 5th power gives the same final two digits.

Powers of $5,10,\mathrm{15.......90},95,100$ will all have $01$ as the final two digits.

Therefore the last two digits of ${21}^{100}$ are $01$