Solution - Base conversion

$${\left(6C7\right)}_{16}$$

Expand digits with place-value powers in the source base.

$$6\cdot {16}^2+12\cdot {16}^1+7\cdot {16}^0$$

Sum the expanded terms to obtain the base-10 value.

$$1735$$

Expand each digit by place value: $$6·{16}^2$$
+ $$12·{16}^1$$
+ $$7·{16}^0$$. This gives $$1,735$$ in base 10.

$$1735\left(base10\right)$$

Use repeated division by the target base.

$$\frac{1735}{10}$$

Record quotient and remainder for this division cycle.

$$1735=10\cdot 173+5$$

Record quotient and remainder for this division cycle.

$$173=10\cdot 17+3$$

Record quotient and remainder for this division cycle.

$$17=10\cdot 1+7$$

Record quotient and remainder for this division cycle.

$$1=10\cdot 0+1$$

Read remainders from last to first to form target-base digits.

$$1735$$

Final converted representation in the target base.

$${\left(1735\right)}_{10}$$

Repeatedly divide $$1,735$$ by $$10$$, collect remainders, and read them in reverse to get $$1,735$$.