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Kavya needs a number that 6 divides exactly but 9 does not. Which of these four numbers fits what she needs?

Class 6Playing with NumbersPlaying with Numbers
  • A234
  • B258
  • C270
  • D342

Step-by-Step Solution

258 is even and 2 + 5 + 8 = 15 is a multiple of 3, so 258 ÷ 6 = 43 exactly; but 15 is not a multiple of 9, so 9 does not divide it. The trap is that 234, 270 and 342 all have digit sum 9, which lets them clear the 9-test as well as the 6-test.
Answer: B) 258

Key idea: HCF and LCM — the two ends of common ground

**HCF** (Highest Common Factor) is the biggest number that divides both numbers — it sits at the *small* end of common factors. **LCM** (Least Common Multiple) is the smallest number both numbers divide — it sits at the *small* end of common multiples (which is the *big* side of factors). For Class 6, the simplest method is listing: write all the factors (or first several multiples) of each number and pick the right one. Faster methods come in Class 7.

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