To solve the problem of converting [tex]\(360_{10}\)[/tex] (a base 10 number) into a different base, specifically base 8, we need to carry out a division process where we repeatedly divide by 8 and keep track of the coefficients and remainders.
1. Start with the initial decimal number [tex]\(360\)[/tex].
2. Divide [tex]\(360\)[/tex] by [tex]\(8\)[/tex].
3. Record the coefficient from this division.
Step-by-Step Solution:
1. Initial Division:
- Divide [tex]\(360\)[/tex] by [tex]\(8\)[/tex]:
[tex]\[
360 \div 8 = 45 \quad \text{(quotient)}
\][/tex]
Here, the result of the division is 45.
So, when converting [tex]\(360_{10}\)[/tex] to base 8, the major coefficient derived in this process is [tex]\(45\)[/tex]. This value indicates the quantity obtained from dividing the given decimal number by the target base.
