Multiply 235base6 and 43 base6
To multiply two numbers in base 6, we can use the same process as multiplication in base 10. However, we need to remember the base and carry over any values greater than or equal to 6.
Let's convert the given numbers into base 10 to make the calculations easier:
235 base 6 = 2 * 6^2 + 3 * 6^1 + 5 * 6^0 = 72 + 18 + 5 = 95
43 base 6 = 4 * 6^1 + 3 * 6^0 = 24 + 3 = 27
Now we can multiply the converted numbers in base 10:
95 * 27 = 2565
Finally, let's convert the result back to base 6:
2565 base 6 = 5 * 6^3 + 2 * 6^2 + 1 * 6^1 + 5 * 6^0 = 1080 + 72 + 6 + 5 = 1163 base 6
So, the multiplication of 235 base 6 and 43 base 6 is 1163 base 6.
To multiply two numbers in base 6, follow these steps:
Step 1: Write down the two numbers, lining them up on the right side.
2 3 5 (base 6)
× 4 3 (base 6)
__________
Step 2: Multiply the rightmost digit of the bottom number (3 in this case) by each digit in the top number.
2 3 5 (base 6)
× 4 3 (base 6)
__________
7 1 5 (base 6) ---- (3 * 235)
Step 3: Multiply the next digit of the bottom number (4 in this case) by each digit in the top number, but shift the result one position to the left.
2 3 5 (base 6)
× 4 3 (base 6)
__________
9 4 0 (base 6) ---- (4 * 235, shifted 1 position to the left)
Step 4: Add the results obtained from Steps 2 and 3.
2 3 5 (base 6)
× 4 3 (base 6)
__________
9 4 0 (base 6)
+ 7 1 5 (base 6)
__________
10 0 5 5(base 6) ---- (Result of step 2 + Result of step 3)
So, 235(base 6) multiplied by 43(base 6) equals 10055(base 6).