Question

4( power 61 ) + 4( power 62 ) + 4( power 63 ) + 4( power 64 ) is divisible by :
A. 3
B. 10
C. 11
D. 13

Answer 1

=4^61+4^62+4^63+4^64

=4^60{4^1+4^2+4^3+4^4}

=4^60{4+16+64+256}

=4^60{340}

We know that 340 is divisible by 10.

[4^60{340}]/10=4^60{34}

Hence (4^61+4^62+4^63+4^64) is divisible by 10.

Answer 2

Given:

A mathematical operation 4( power 61 ) + 4( power 62 ) + 4( power 63 ) + 4( power 64 ).

To Find:

The sum of the above expression is divisible by which number among the given options?

Solution:

The given problem can be solved by using the concepts of exponents and divisibility rules.

1. The given expression is$4^{61}+4^{62} +4^{63} +4^{64}$,

2. The given expression can also be written as,

=>$4^{60}(4+4^2+4^3+4^4),$

=>$4^{60}(4+16+64+256),$

=>$4^{60}(260+ 80),$

=>$4^{60}(340).$

3. The value$4^{60}*340$ can also be written as$4^{60}(34 * 10)$,

=> The above value is divisible by 10 because 10 is a factor of the given number.

4. For a number to be divisible by 10 the units digit of the number must be zero in all the cases. ( Same as the above case).

5. Hence, the given operation is divisible by 10.

Therefore, the given value is divisible by 10. Option C is the correct answer.