Question

determine whether 306 is divisible by 2, 3, 4, or 6. 3 and 6 only 2, 3, and 6 only 2 and 3 only 2, 3, 4, and 6

Explanation:

Step1: Check divisibility by 2

A number is divisible by 2 if its last digit is even. 306 ends in 6 (even), so $\frac{306}{2}=153$ (integer, divisible).

Step2: Check divisibility by 3

A number is divisible by 3 if the sum of its digits is divisible by 3. Sum: $3+0+6=9$, $\frac{9}{3}=3$ (integer), so $\frac{306}{3}=102$ (divisible).

Step3: Check divisibility by 4

A number is divisible by 4 if its last two digits form a number divisible by 4. Last two digits: 06=6, $\frac{6}{4}=1.5$ (not integer, not divisible).

Step4: Check divisibility by 6

A number is divisible by 6 if divisible by both 2 and 3. 306 is divisible by 2 and 3, so $\frac{306}{6}=51$ (divisible).

Answer:

2, 3, and 6 only