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The factors of 28 apart from 28 itself are 1, 2, 4, 7 and 14. What do they add up to, and what does that tell you about 28?

Class 6Playing with NumbersPlaying with Numbers
  • A27, which is one short of 28
  • B56, because 28 itself has to be counted in as well
  • C28, exactly equal to the number — and that is what makes 28 a perfect number
  • D28, which proves that 28 is a prime number

Step-by-Step Solution

1 + 2 + 4 + 7 + 14 = 28, landing exactly on the number itself — that is what 'perfect' means, and 6 = 1 + 2 + 3 is the only smaller example. One trap is counting 28 in as well, which gives 56; the other is muddling 'perfect' with 'prime' — 28 has six factors, so it is composite.
Answer: C) 28, exactly equal to the number — and that is what makes 28 a perfect number

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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