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A number is divisible by 6. Which statement must be true?

Class 6Playing with NumbersPlaying with Numbers
  • AIt is divisible by both 2 and 3.
  • BIt is divisible by 4.
  • CIt is divisible by 9.
  • DIt is an odd number.

Step-by-Step Solution

Since , any number divisible by 6 is divisible by both 2 and 3. It need not be divisible by 4 or 9, and it is even (not odd).
Answer: A) It is divisible by both 2 and 3.

Key idea: Quick divisibility tests

Some checks are so fast you can do them in your head:

- **By 2**: the last digit is even (0, 2, 4, 6, or 8).
- **By 3**: the sum of the digits is divisible by 3. (273 → 2 + 7 + 3 = 12 → 12 ÷ 3 = 4 ✓)
- **By 5**: the last digit is 0 or 5.
- **By 9**: the sum of the digits is divisible by 9.
- **By 10**: the last digit is 0.
- **By 4**: the last two digits form a number divisible by 4.

These let you spot factors without doing the full division.

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