Which among the following is exactly divisible by 6?
2025
Which among the following is exactly divisible by 6?
Answer: A. 235686 — A whole number is divisible by 6 if and only if it is divisible by both 2 and 3 at the same time: divisibility by 2 depends only on whether the last digit is…
- A.
235686
- B.
267
- C.
3675
- D.
6872
Attempted by 19 students.
Show answer & explanation
Correct answer: A
A whole number is divisible by 6 if and only if it is divisible by both 2 and 3 at the same time: divisibility by 2 depends only on whether the last digit is even, and divisibility by 3 depends only on whether the sum of all its digits divides evenly by 3.
Number | Last digit (even → ÷2 ok?) | Digit sum (÷3 ok?) | Divisible by 6? |
|---|---|---|---|
235686 | 6 → even, divisible by 2 | 2+3+5+6+8+6 = 30 → divisible by 3 | Yes |
267 | 7 → odd, NOT divisible by 2 | 2+6+7 = 15 → divisible by 3 | No (fails ÷2) |
3675 | 5 → odd, NOT divisible by 2 | 3+6+7+5 = 21 → divisible by 3 | No (fails ÷2) |
6872 | 2 → even, divisible by 2 | 6+8+7+2 = 23 → NOT divisible by 3 | No (fails ÷3) |
Direct division confirms this: 235686 ÷ 6 = 39281 exactly, with no remainder, while 267 ÷ 6 = 44.5, 3675 ÷ 6 = 612.5, and 6872 ÷ 6 = 1145.33… all leave a remainder.
So 235686 is the number exactly divisible by 6.