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Which divisibility test confirms that 234 is divisible by 3?

Class 6Playing with NumbersPlaying with Numbers
  • A234 ends in 4, which is even.
  • BSum of digits is 2 + 3 + 4 = 9, which is divisible by 3.
  • C234 is greater than 3.
  • D234 ÷ 2 has no remainder.

Step-by-Step Solution

Divisibility by 3 is checked via the digit-sum rule. 2+3+4 = 9, divisible by 3, so 234 is divisible by 3.
Answer: B) Sum of digits is 2 + 3 + 4 = 9, which is divisible by 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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