Multiple choice general knowledge math & puzzles

Find the remainder when (3264)in base 7 is divided by (8) in base 10

  1. 0

  2. 2

  3. 3

  4. 5

  5. 1
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

(3264) in base 7 is 3(7^3) + 2(7^2) + 6(7^1) + 4(7^0) = 1029 + 98 + 42 + 4 = 1173 in base 10. 1173 divided by 8 is 146 with a remainder of 5. The other options are incorrect remainders.

AI explanation

To find the remainder when a number in one base is divided by a number in another base, we need to convert both numbers to the same base. In this case, we need to convert (3264) from base 7 to base 10.

To convert (3264) from base 7 to base 10, we can use the following formula:

$(3 \times 7^3) + (2 \times 7^2) + (6 \times 7^1) + (4 \times 7^0)$

Simplifying the equation, we get:

$1029 + 98 + 42 + 4 = 1173$

So, (3264) in base 7 is equal to 1173 in base 10.

Now, we need to find the remainder when 1173 is divided by 8 in base 10.

To find the remainder, we can divide 1173 by 8:

$1173 \div 8 = 146 \text{ remainder } 5$

Therefore, the remainder when (3264) in base 7 is divided by (8) in base 10 is 5.

The correct answer is option D.

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