Example

Example of Simplifying a Fraction Using Prime Factorization

When it is difficult to find common factors between a numerator and denominator, simplify the fraction by factoring both into prime numbers first. For example, to simplify 315770-\frac{315}{770}, rewrite it using prime factorizations: 335725711-\frac{3 \cdot 3 \cdot 5 \cdot 7}{2 \cdot 5 \cdot 7 \cdot 11}. Next, divide out the common factors of 55 and 77 using the Equivalent Fractions Property. Finally, multiply the remaining factors in the numerator (33=93 \cdot 3 = 9) and the denominator (211=222 \cdot 11 = 22) to obtain the simplified fraction 922-\frac{9}{22}.

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Updated 2026-05-02

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