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Every factor of an odd number is itself odd. Which list below could be the complete set of factors of an odd number?

Class 6Playing with NumbersPlaying with Numbers
  • A1, 3, 9, 27
  • B1, 2, 3, 6
  • C1, 2, 4, 8
  • D1, 5, 10, 50

Step-by-Step Solution

These are the factors of 27, and every one of them is odd. Each other list contains an even number, and an even factor would force the number itself to be even , so 50 is even). The trap is forgetting that the number itself is on its own factor list and must obey the rule too.
Answer: A) 1, 3, 9, 27

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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