Which of the following numbers is divisible by 24?

Given data

• Divisibility by 24 requires divisibility by 3 and by 8 (since 24 = 3 × 8 and gcd(3,8)=1).

Checks

312: last three digits 312 ⇒ 312 ÷ 8 = 39 (integer), digit sum 3+1+2=6 ⇒ /3 yes ⇒ /24 yes.444: 444 ÷ 8 = 55 remainder 4 ⇒ not /8 ⇒ not /24.520: 520 ÷ 8 = 65 (ok) but digit sum 5+2+0=7 ⇒ not /3 ⇒ not /24.458: 458 ÷ 8 not integer; digit sum 17 ⇒ not /3 ⇒ not /24.

Final Answer

Number divisible by 24 is 312.