Solution - Base conversion

$${\left(4F2\right)}_{16}$$

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

$$4\cdot {16}^2+15\cdot {16}^1+2\cdot {16}^0$$

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

$$1266$$

Expand each digit by place value: $$4·{16}^2$$
+ $$15·{16}^1$$
+ $$2·{16}^0$$. This gives $$1,266$$ in base 10.

$$1266\left(base10\right)$$

Use repeated division by the target base.

$$\frac{1266}{10}$$

Record quotient and remainder for this division cycle.

$$1266=10\cdot 126+6$$

Record quotient and remainder for this division cycle.

$$126=10\cdot 12+6$$

Record quotient and remainder for this division cycle.

$$12=10\cdot 1+2$$

Record quotient and remainder for this division cycle.

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

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

$$1266$$

Final converted representation in the target base.

$${\left(1266\right)}_{10}$$

Repeatedly divide $$1,266$$ by $$10$$, collect remainders, and read them in reverse to get $$1,266$$.