Question

what is the remainder when 7^23+7^24+7^25+7^26 is divided by16​

Answer 1

Answer:

0

Step-by-step explanation:

7²³+7²⁴+7²⁵+7²⁶

= 7²³(1 + 7 + 7²+ 7³)

= 7²³(1+7+49+343) = 7²³*400.

Since 400 is divisible by 16, the remainder is 0.

Answer 2

Therefore the remainder is '0' when 7²³ + 7²⁴ + 7²⁵ + 7²⁶ is divided by 16.

Given:

The number: 7²³ + 7²⁴ + 7²⁵ + 7²⁶

To Find:

The remainder when  7²³ + 7²⁴ + 7²⁵ + 7²⁶ is divided by 16

Solution:

The given question can be solved as shown below.

Given number: 7²³ + 7²⁴ + 7²⁵ + 7²⁶

⇒ 7²³ + 7²⁴ + 7²⁵ + 7²⁶ = 7²³ ( 1 + 7 + 7²+ 7³ ) = 7²³ ( 1 + 7 + 49 + 343 ) = 7²³ × 400.

So 7²³ + 7²⁴ + 7²⁵ + 7²⁶ =  7²³ × 400

Now ( 7²³ + 7²⁴ + 7²⁵ + 7²⁶ ) / 16 = 7²³ × 400 / 16 = 7²³ × 25

So the remainder is 'zero' because 400 is divided by 16.

Therefore the remainder is '0' when 7²³ + 7²⁴ + 7²⁵ + 7²⁶ is divided by 16.

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