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Factors normally come in pairs, so most numbers have an even count of factors. Which of these numbers breaks that pattern and has an ODD number of factors?

Class 6Playing with NumbersPlaying with Numbers
  • A12
  • B20
  • C40
  • D36

Step-by-Step Solution

Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36 — nine of them. Factors usually pair up (1 with 36, 2 with 18, 3 with 12, 4 with 9), but 6 pairs with itself because , leaving one factor unpaired. The trap is assuming every number has an even count: 12 and 20 have 6 factors each and 40 has 8.
Answer: D) 36

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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