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What is the remainder when 4^{17} is divided by 7?

Explanation	Calculations	Help
$We translate the phrase "remainder when 4^{17} is divided by 7" into an equation relating the divisor, quotient, and remainder.$	$7 k + r = 4^{17}$	Theory & Tactics Method Card TRANS5-F Click to view full details
$We calculate the remainder when 4^{3} is divided by 7.$	$4^{3} = 64 = 7 \times 9 + 1 remainder of 4^{3} divided by 7 = 1$	Theory & Tactics Method Card DIV4-D Click to view full details
$We express 4^{17} as (4^{3})^{5} \times 4^{2} and use the remainders of 4^{3} and 4^{2} to find the remainder of the entire expression.$	$4^{17} = (4^{3})^{5} \times 4^{2} = (7 \times 9 + 1)^{5} \times 4^{2} 4^{2} = 16 = 7 \times 2 + 2 remainder = 1^{5} \times 2 = 2$	Theory & Tactics Method Card DIV4-D Click to view full details

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C

What is the remainder when 4^{17} is divided by 7?

Explanation	Calculations	Help
$We translate the phrase "remainder when 4^{17} is divided by 7" into an equation relating the divisor, quotient, and remainder.$	$7 k + r = 4^{17}$	Theory & Tactics Method Card TRANS5-F Click to view full details
$We calculate the remainder when 4^{3} is divided by 7.$	$4^{3} = 64 = 7 \times 9 + 1 remainder of 4^{3} divided by 7 = 1$	Theory & Tactics Method Card DIV4-D Click to view full details
$We express 4^{17} as (4^{3})^{5} \times 4^{2} and use the remainders of 4^{3} and 4^{2} to find the remainder of the entire expression.$	$4^{17} = (4^{3})^{5} \times 4^{2} = (7 \times 9 + 1)^{5} \times 4^{2} 4^{2} = 16 = 7 \times 2 + 2 remainder = 1^{5} \times 2 = 2$	Theory & Tactics Method Card DIV4-D Click to view full details

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C