Reduce 256/144 to lowest terms
Reduce 256/144 to lowest terms.
In order to simplify the fraction 256/144 to its simplest form, it is necessary to determine the greatest common divisor (GCD) of the numerator (256) and the denominator (144). Once the GCD is found, both the numerator and the denominator should be divided by it.
The prime factorization of 256 is 2^8, while the prime factorization of 144 is 2^4 * 3^2. The common factors between them are 2^4, resulting in a GCD of 16.
Consequently, both the numerator and the denominator should be divided by 16:
(256 ÷ 16) / (144 ÷ 16) = 16/9
Therefore, the fraction 256/144, when reduced to its simplest form, is 16/9.
The numerator and denominator of the fraction 256/144 can be divided by their greatest common divisor (GCD). By dividing both 256 and 144 by their GCD, which is 16, the fraction can be simplified. Simplifying the fraction 256/144 involves dividing both the numerator and the denominator by their GCD, which is 16.
Dividing both by 16:
(256 ÷ 16) / (144 ÷ 16) = 16 / 9
So, 256/144 simplifies to 16/9.
If you wish to simplify a fraction to its most reduced form, there is a formula that can be utilized.
\[ \text{Reduced Fraction} = \frac{\text{Numerator}}{\text{GCD(Numerator, Denominator)}} \div \frac{\text{Denominator}}{\text{GCD(Numerator, Denominator)}} \]
In the case of \( \frac{256}{144} \):
\[ \text{GCD(256, 144)} = 16 \]
\[ \text{Reduced Fraction} = \frac{256}{16} \div \frac{144}{16} = \frac{16}{9} \]
The formula essentially requires dividing both the numerator and denominator of the fraction by their greatest common divisor (GCD).
To simplify or decrease a fraction, adhere to the following instructions:
1. Determine the Greatest Common Divisor (GCD): Determine the GCD of the numerator and the denominator. This is the largest number that evenly divides both the numerator and denominator.
2. Divide by the GCD: Divide both the numerator and the denominator by the GCD obtained in step 1.
3. Express the Fraction in Reduced Form: Represent the fraction in its simplified form, where the numerator and denominator do not share any factors other than 1.
Here’s a step-by-step example using \( \frac{256}{144} \):
a. **Find the GCD:**
– The prime factorization of 256 is \(2^8\).
– The prime factorization of 144 is \(2^4 \times 3^2\).
– The common factors are \(2^4\), so the GCD is \(2^4 = 16\).
b. **Divide by the GCD:**
– \( \frac{256}{144} \) ÷ \( \frac{16}{16} \) = \( \frac{16}{9} \)
c. **Write the Reduced Fraction:**
– \( \frac{256}{144} \) simplifies to \( \frac{16}{9} \).
To simplify the fraction, it is important to divide both the numerator and denominator by their greatest common divisor.
