Study Guides/Maths/Factors of 27
Study Guide · Maths

What are the Factors of 27?

In mathematics, the 'factors' of a number are simply all the integers (whole numbers) that can perfectly divide that number without leaving any remainder.

Question (Click to Flip)

Can factors be negative?

Answer

Yes. While we usually only ask for positive factors in school, mathematically, two negative numbers multiplied together give a positive. So the negative factors of 27 are: -1, -3, -9, and -27.

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Key Facts

1 is the universal factor. It is a factor of every single number in existence.

Every number is a factor of itself.

1. What are the Factors of 27?

The number 27 is a composite number. It has exactly 4 positive factors. The factors of 27 are: 1, 3, 9, and 27.

2. Step-by-Step Calculation (How did we find them?)

To find the factors, we test dividing 27 by numbers starting from 1:

  • $27 \div 1 = 27$ (Remainder is 0. So, 1 and 27 are factors).
  • $27 \div 2 = 13.5$ (It leaves a remainder/decimal because 27 is an odd number. So, 2 is NOT a factor).
  • $27 \div 3 = 9$ (Remainder is 0. So, 3 and 9 are factors).
  • If we check 4, 5, 6, 7, and 8, none of them divide 27 perfectly.
  • We stop checking once we reach 9, because we already found 9 in our previous division.

3. Factor Pairs of 27

Factors always come in pairs that multiply together to give the original number.

  • $(1 \times 27) = 27$
  • $(3 \times 9) = 27$ Therefore, the positive factor pairs are (1, 27) and (3, 9).

4. Prime Factorization of 27

Prime factorization means breaking the number down until only prime numbers are left. Since 27 is $3 \times 9$, and 9 is $3 \times 3$: The prime factorization of 27 is: $3 \times 3 \times 3$ (or $3^3$).

Questions and Answers

Can factors be negative?+

Yes. While we usually only ask for positive factors in school, mathematically, two negative numbers multiplied together give a positive. So the negative factors of 27 are: -1, -3, -9, and -27.

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