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Mrs Iyer lined up her class in rows of 7, and one student was left over (orange). Count all the students. Can she arrange ALL of them in equal rows, with at least 2 rows and at least 2 students in each row?

Class 6Playing with NumbersPlaying with Numbers
  • AYes, 4 rows of 7
  • BYes, 3 rows of 10
  • CNo, because 29 is a prime number
  • DYes, 5 rows of 6

Step-by-Step Solution

There are students. The only factors of 29 are 1 and 29, so 29 is prime and cannot make a rectangle of rows. (4 rows of 7 forgets the extra student; 3 rows of 10 and 5 rows of 6 need 30.)
Answer: C) No, because 29 is a prime number

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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