Question

Multiply 3461 × 234 in base 8

Answer 1

[AI-generated answer — Bot GPT 3.5]

To multiply 3461 by 234 in base 8, follow these steps:

Step 1: Convert the numbers to decimal form
3461 in base 8 is equal to 1889 in decimal form.
234 in base 8 is equal to 156 in decimal form.

Step 2: Multiply the numbers in decimal form
Multiply 1889 by 156:
1889 * 156 = 294684

Step 3: Convert the result back to base 8
294684 in decimal form is equal to 1073434 in base 8.

Therefore, 3461 multiplied by 234 in base 8 is equal to 1073434.

Answer 2

[AI-generated answer — Explain Bot]

To multiply numbers in base 8, we follow the same basic principles as multiplying numbers in base 10, or decimal system. We can use the long multiplication method to multiply 3461 by 234 in base 8.

Here's the step-by-step process:

Step 1: Write the numbers vertically, aligning them on the right side.

3461
× 234

Step 2: Start multiplication by multiplying the rightmost digit of the bottom number (234) by each digit of the top number (3461) from right to left.

3461
× 234
-------
6922

Step 3: Multiply the second digit from the right of the bottom number (234) by each digit of the top number (3461). Shift the result one position to the left and write it below the first partial product.

3461
× 234
-------
69220

Step 4: Multiply the third digit from the right of the bottom number (234) by each digit of the top number (3461). Shift the result two positions to the left and write it below the previous partial product.

3461
× 234
-------
92418
+------
807382

Therefore, the product of 3461 multiplied by 234 in base 8 is 807382.

Answer 3

[AI-generated answer — Step-by-Step Bot]

To multiply 3461 by 234 in base 8, let's break it down step-by-step:

Step 1: Convert the numbers to base 10.
3461 in base 8 is equal to (3 × 8^3) + (4 × 8^2) + (6 × 8^1) + (1 × 8^0) = 1865.
234 in base 8 is equal to (2 × 8^2) + (3 × 8^1) + (4 × 8^0) = 156.

Step 2: Multiply the numbers in base 10.
1865 × 156 = 290040.

Step 3: Convert the result back to base 8.
To convert 290040 to base 8, we divide 290040 by 8 repeatedly until the quotient is zero.

290040 ÷ 8 = 36255 remainder 0
36255 ÷ 8 = 4531 remainder 7
4531 ÷ 8 = 566 remainder 3
566 ÷ 8 = 70 remainder 6
70 ÷ 8 = 8 remainder 6
8 ÷ 8 = 1 remainder 0
1 ÷ 8 = 0 remainder 1

Reading the remainders in reverse order gives us 1063760.

Therefore, 3461 in base 8 multiplied by 234 in base 8 is equal to 1063760 in base 8.