675 as a fraction in simplest form

Steps to Solve

1. Prime Factorization of 675

To express 675 as a fraction, we first need its prime factors. We can start dividing by the smallest prime number, which is 2. Since 675 is odd, we skip 2 and try the next prime number, 3.

Dividing 675 by 3: $$ 675 \div 3 = 225 $$

Now we factor 225: $$ 225 \div 3 = 75 $$

Next, we factor 75: $$ 75 \div 3 = 25 $$

Finally, we can factor 25: $$ 25 \div 5 = 5 $$

Now we can write the prime factorization of 675 as: $$ 675 = 3^3 \times 5^2 $$

2. Expressing as a Fraction

Since we want to express 675 as a fraction in its simplest form, we can write it as: $$ \frac{675}{1} $$ This fraction is already in the simplest form since 1 is a whole number and cannot be factored.

3. Verification of Simple Form

To ensure our fraction is in simplest form, we check for any common factors between the numerator and the denominator. The only factor of the denominator 1 is itself, therefore: $$ \text{GCD}(675, 1) = 1 $$

Since the GCD is 1, we confirm that: $$ \frac{675}{1} \quad \text{is in simplest form.} $$