Question
simply x 675 divided by x 453
Answers
Answered by
GPT-4o mini
To simplify the expression \( \frac{675}{453} \), we can find the greatest common divisor (GCD) of the two numbers and divide both the numerator and the denominator by that GCD.
1. **Finding the GCD**:
- The prime factorization of 675 is \( 3^3 \times 5^2 \).
- The prime factorization of 453 is \( 3^2 \times 151 \).
The GCD is the product of the lowest powers of the common prime factors:
- For 3, the lowest power is \( 3^2 \).
- 5 and 151 do not appear in both factorizations.
Thus, the GCD of 675 and 453 is \( 3^2 = 9 \).
2. **Dividing both numbers by the GCD**:
\[
\frac{675 \div 9}{453 \div 9} = \frac{75}{51}
\]
3. **Further simplifying \( \frac{75}{51} \)**:
- The prime factorization of 75 is \( 3 \times 5^2 \).
- The prime factorization of 51 is \( 3 \times 17 \).
The GCD of 75 and 51 is 3.
Dividing both numbers by 3 gives:
\[
\frac{75 \div 3}{51 \div 3} = \frac{25}{17}
\]
Thus, the simplified form of \( \frac{675}{453} \) is \( \frac{25}{17} \).
1. **Finding the GCD**:
- The prime factorization of 675 is \( 3^3 \times 5^2 \).
- The prime factorization of 453 is \( 3^2 \times 151 \).
The GCD is the product of the lowest powers of the common prime factors:
- For 3, the lowest power is \( 3^2 \).
- 5 and 151 do not appear in both factorizations.
Thus, the GCD of 675 and 453 is \( 3^2 = 9 \).
2. **Dividing both numbers by the GCD**:
\[
\frac{675 \div 9}{453 \div 9} = \frac{75}{51}
\]
3. **Further simplifying \( \frac{75}{51} \)**:
- The prime factorization of 75 is \( 3 \times 5^2 \).
- The prime factorization of 51 is \( 3 \times 17 \).
The GCD of 75 and 51 is 3.
Dividing both numbers by 3 gives:
\[
\frac{75 \div 3}{51 \div 3} = \frac{25}{17}
\]
Thus, the simplified form of \( \frac{675}{453} \) is \( \frac{25}{17} \).