How do you use prime factorization to reduce a fraction?
What don't you understand about my previous answer?
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factor the numerator and the denominator, then cancel values which appear in both places.
for example,
810/36 = 2*3^4*5/2^2*3^2 = 3^2*5/2 = 45/2
To use prime factorization to reduce a fraction, you need to find the greatest common factor (GCF) of the numerator and the denominator. Here's how you can do it:
1. Write down the prime factorization of both the numerator and the denominator.
- Prime factorization involves expressing a number as a product of its prime factors.
- For example, if the numerator is 24, you can write it as 2^3 * 3^1 since 24 can be expressed as (2 * 2 * 2) * 3.
- Similarly, if the denominator is 36, the prime factorization would be 2^2 * 3^2.
2. Identify the common prime factors in both the numerator and the denominator.
- In the example above, the common prime factors are 2 and 3.
3. Take the lowest exponent for each common prime factor from the numerator and denominator.
- In this case, the lowest exponent for 2 is 2, and the lowest exponent for 3 is 1.
4. Multiply the common prime factors with the respective lowest exponents.
- Therefore, the GCF would be 2^2 * 3^1, which is equal to 12.
5. Divide both the numerator and the denominator of the fraction by the GCF obtained in the previous step.
- This means dividing both 24 and 36 by 12.
By following these steps, you will be able to reduce a fraction using prime factorization. In this example, the fraction would be reduced from 24/36 to 2/3.