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A school in Nagpur has 42 boys and 56 girls in Class 6. The teacher makes teams so that every team has the same number of boys and the same number of girls, with no child left out. What is the greatest number of teams possible?

Class 6Playing with NumbersPlaying with Numbers
  • A7
  • B98
  • C168
  • D14

Step-by-Step Solution

The number of teams must divide both 42 and 56, and it should be as large as possible — the HCF. Since and , the HCF is , giving each team 3 boys and 4 girls. The traps: 7 is a common factor but not the highest, 98 is 42 + 56, and 168 is the LCM.
Answer: D) 14

Key idea: Factors come in pairs

To find every factor of a number, walk up from 1 and check each whole number — if it divides the number with no remainder, it is a factor. Factors come in **pairs**: if 4 is a factor of 12, so is 12 ÷ 4 = 3. So you only need to check up to the square root of the number to find them all. Factors of 12: — six factors total: 1, 2, 3, 4, 6, 12. Every number has 1 and itself as factors.

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