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What is the remainder when 4^{47} is divided by 7?

Explanation	Calculations	Help
$We translate the phrase "remainder when 4^{47} is divided by 7" into an equation relating the divisor, quotient, and remainder.$	$7 k + r = 4^{47}$	Theory & Tactics Method Card TRANS5-F Click to view full details
$We calculate the remainder when 4 cubed is divided by 7.$	$4^{3} = 64 64 = 7 \times 9 + 1 remainder = 1$	Theory & Tactics Method Card DIV4-D Click to view full details
$We express the exponent 47 as 3 \times 15 plus 2 and use the previous result to find the remainder of 4 to the 47th power.$	$4^{47} = (4^{3})^{15} \times 4^{2} (4^{3})^{15} = (7 \times 9 + 1)^{15} remainder = 1^{15} \times 4^{2} = 16 16 = 7 \times 2 + 2 remainder = 2$	Theory & Tactics Method Card DIV4-D Click to view full details

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C

What is the remainder when 4^{47} is divided by 7?

Explanation	Calculations	Help
$We translate the phrase "remainder when 4^{47} is divided by 7" into an equation relating the divisor, quotient, and remainder.$	$7 k + r = 4^{47}$	Theory & Tactics Method Card TRANS5-F Click to view full details
$We calculate the remainder when 4 cubed is divided by 7.$	$4^{3} = 64 64 = 7 \times 9 + 1 remainder = 1$	Theory & Tactics Method Card DIV4-D Click to view full details
$We express the exponent 47 as 3 \times 15 plus 2 and use the previous result to find the remainder of 4 to the 47th power.$	$4^{47} = (4^{3})^{15} \times 4^{2} (4^{3})^{15} = (7 \times 9 + 1)^{15} remainder = 1^{15} \times 4^{2} = 16 16 = 7 \times 2 + 2 remainder = 2$	Theory & Tactics Method Card DIV4-D Click to view full details

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C