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Find the remainder when 5^400 is divided by 19

User Smartse
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2 Answers

4 votes

Final answer:

To find the remainder when 5^400 is divided by 19, divide the exponent (400) by 18 to find a quotient of 22 and a remainder of 4. Therefore, the remainder is 4.

Step-by-step explanation:

To find the remainder when 5400 is divided by 19, we can use the concept of modular arithmetic.

We start by computing the remainders of 5 raised to the powers of 1, 2, 3, 4, and so on, until we spot a pattern.

We notice that the remainders repeat every 18 powers of 5. Therefore, to find the remainder when 5400 is divided by 19, we divide the exponent (400) by 18 to get a quotient of 22 and a remainder of 4.

So, the remainder when 5400 is divided by 19 is 4.

User Brandon Rhodes
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8.4k points
2 votes

Answer:

the remainder is 0

Step-by-step explanation:

User Ruben Lopez
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8.5k points

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