How to Factor a Fraction


A fraction could potentially have an infinite number of factors, numbers that could be multiplied together to achieve the desired fraction. Fractions cannot as a whole be factored. However, factoring the numerator and denominator of a fraction separately is an important tool in simplifying rational numbers.

Things You'll Need

  • Pencil
  • Paper
  • Write down the fraction that needs to be reduced. For the sake of example we'll use "27/45."

  • Prime factorize the numerator by finding the smallest possible numbers that can be multiplied together to create the numerator. In our case, the prime factorization of 27 is three cubed.

  • Prime factorize the denominator. In our case, the prime factorization of 45 is three squared times 5.

  • Rewrite the fraction using the prime factorizations of the numerator and denominator. we thus have "(3x3x3)/(3x3x5)."

  • Cancel equivalent terms in the numerator and the denominator. This leaves us with "3/5" which is the fraction "27/45" in lowest terms.

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