Which of the numbers given below is divisible by 15?

The correct answer is Option (3) → 4365

\(15=3\times5\), and 3 and 5 have no common factor, so a number is divisible by 15 when it is divisible by both 3 and 5. All four numbers end in 5, so all are divisible by 5; the test for 3, the sum of the digits divisible by 3, decides.

• 2365 — 2 + 3 + 6 + 5 = 16, not divisible by 3

• 1375 — 1 + 3 + 7 + 5 = 16, not divisible by 3

• 4365 — 4 + 3 + 6 + 5 = 18, divisible by 3, so 4365 is divisible by 15 (\(4365=15\times291\))

• 2275 — 2 + 2 + 7 + 5 = 16, not divisible by 3