Answer
$4443_{\text{seven}}$
Work Step by Step
The place values of base seven are: $,,,, 7^3, 7^2, 7^1, 1$.
The place values that are less than or equal to $1599$ are $7^3$, $7^2$, $7^1$, and $1$
Divide $1599$ by $7^3$ or $343$ to obtain:
$1599 \div 343 = 4$ remainder $227$
Divide the remainder $227$ by $7^2$ or $49$ to obtain:
$227 \div 49 = 4$ remainder $31$
Divide the remainder $31$ by $7^1$ or $7$ to obtain:
$31 \div 7 = 4$ remainder $3$
Divide the remainder $r$ by $1$ to obtain:
$3 \div 1 = 4$ remainder $0$
Thus,
$1599=(4 \times 7^3) + (4 \times 7^2) + (4 \times 7^1) + (3 \times 1)
\\1599=4443_{\text{seven}}$
