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.
References
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