Question

Product of all the even divisors of $N=1000$, is

• A. $32\cdot {10}^2$
• B. $64\cdot 2^{14}$
• C. $64\cdot {10}^{18}$
• D. $128\cdot {10}^6$

Answer 1

The correct option is A $32\cdot {10}^2$

Product of all even divisors of $1000$

Total maximum divisor $=2^3\times 5^3$

So even divisors are ,

$2,4,8,2\times 5,4\times 5,8\times 5,2\times 25,4\times 25,8\times 25,8\times 125,4\times 125,2\times 125=2^4\times 4^4\times 8^4\times 2^3\times 4^3\times 8^3\times 5^3\times {25}^3\times {125}^3=2^4\times 2^8\times 2^{12}\times 2^3\times 2^6\times 2^9\times 5^3\times 5^6\times 5^9=2^{42}{5}^{18}=2^{18}{2}^{24}{5}^{18}=2^{24}{10}^{18}$