Question

${11}^3+{12}^3+{13}^3$ is divisible by

• A. 11
• B. 16
• C. 13
• D. 36

Answer 1

The correct option is D 36

The given expression is ${11}^3+{12}^3+{13}^3$
Using identity we have
$a^3+b^3+c^3=(a+b+c)(a^2+b^2+c^2-ab-ac-bc)$
Taking a = 11, b = 12, c = 13 we get

${11}^3+{12}^3+{13}^3=(11+12+13)({11}^2+{12}^2+{13}^2-(11\left)\right(12)-(11\left)\right(13)-(12\left)\right(13\left)\right)$

${11}^3+{12}^3+{13}^3=\left(36\right)({11}^2+{12}^2+{13}^2-(11\left)\right(12)-(11\left)\right(13)-(12\left)\right(13\left)\right)$
Since, 36 is one of the factor of the expression, it will be divisible by 36.