Question

${21}^{643}=25A+B.$ Find the least value that B can take?

• A. 11
• B. 1
• C. 6
• D. 16

Answer 1

The correct option is A 11

The question is asking for the remainder when ${21}^{643}$ is divided by 25.
We can use the last two digits technique to get the answer, since the remainder when a number is divided by 25, depends only on the last two digits.

For numbers ending in 1, the last two digits of a power expression $a^b$ can be determined as -

The last digit is always 1.

The $2^{nd}$ last digit = product of tens digit of base * unit digit of the power i.e. ${21}^{643}=......61(6=2\times 3)$

When 61 is divided by 25, the remainder is 11.