4^{11} + 4^{12} + 4^{13} + 4^{14} is divisibl | vedclass

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Question

(C) To find the divisor,factor out the smallest power of $4$,which is $4^{11}$.$4^{11} + 4^{12} + 4^{13} + 4^{14} = 4^{11} (1 + 4^1 + 4^2 + 4^3)$$= 4^

Vedclass · Accepted Answer

$17$

Vedclass · Answer

(C) To find the divisor,factor out the smallest power of $4$,which is $4^{11}$.$4^{11} + 4^{12} + 4^{13} + 4^{14} = 4^{11} (1 + 4^1 + 4^2 + 4^3)$$= 4^{11} (1 + 4 + 16 + 64)$$= 4^{11} (85)$Since $85 = 5 	imes 17$,the expression is $4^{11} 	imes 5 	imes 17$.Therefore,the expression is divisible by $17$.

$4^{11} + 4^{12} + 4^{13} + 4^{14}$ is divisible by:

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