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What is the largest three-digit number that is divisible by both 2 and 5?

Class 6Playing with NumbersPlaying with Numbers
  • A990
  • B995
  • C998
  • D1,000

Step-by-Step Solution

A number divisible by both 2 and 5 is divisible by 10, so it must end in 0. The largest three-digit number ending in 0 is . The traps: 995 passes only the 5-test, 998 only the 2-test, and 1,000 passes both tests but has four digits.
Answer: A) 990

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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