Question

find the remainder when 2^21 is divided by 6. a. 0 b. 1 c. 2 d. 3

Answer 1

Answer:2

Simply we know that 2^21=2097152

Then divide this by 6

Which gives u remainder 2

Answer 2

Option C (2) is the correct answer.

The given question can be solved using the divisibility principle.

• It is given that$2^{21}$ is divided by 6.

• $2^{21}$ can be further written as follows,

=> $2^{21}$ = $2^{20}$ x 2,

=> $2^{21}$ = $4^{10}$ x 2,

=> $2^{21}$ = $16^{5}$ x 2,

=> $2^{21}$ = $16^4$ x 16 x 2,

=> $2^{21}$ = $16^4$ x 32,

=> $2^{21}$ = $256^2$ x 32,

=> $2^{21}$ = 65536 x32,

=> $2^{21}$ = 2097152.

• A number is divisible by 6 only when the number is divisible by both 2 and 3.
• A number is divisible by 2 if the last digit is even. A number is divisible by 3 is the sum of the digits are divisible by 3.

• The value of the given expression is 2097152. The sum of the digits of the obtained number is 26. Hence it is not divisible by 3. ( A number is said to be divisible by 3 only if the sum of the digits are divisible by 3). Hence the number is not divisible by 6 as it is not divisible by 3.

=> Remainder = (2097152/6),

=> Remainder  = 2.

=> 2097152 = 349525 x 6 + 2.

Therefore the remainder when$2^{21}$ is divided by 6 is 2.