800/75 Simplified

Learn how to find what is 800/75 simplified as a fraction just in a few minutes. We have covered why the GCF or factorization is important to simplify 800/75 in simplest form.

To reduce 800/75 in its lowest terms, you must be familiar with either how to find the greatest common factor or prime factors. Both of these methods are used to recognize if 800/75 can be reduced in simplest form. In this case, the (greatest common factor) GDF of 800 and 75 is 25. Dividing both the numerator and denominator by GCF, the fraction 800/75 becomes 32/3 which is the simplest form.

800/75 Simplified as a Fraction
Using Factorization:
800/75 = (?)
800/75 = (2 x 2 x 2 x 2 x 2 x 5 x 5)/(3 x 5 x 5)      write 800/75 in terms of factors
= 32/3
800/75 = 32/3
800/75 simplified is 32/3

Using GCF
800/75 = (?)
GCF of 800 and 75 is 25.
800/75 = (800/25)/(75/25)
= 32/3
800/75 = 32/3
800/75 simplified is 32/3 in fraction form
where,
800/75 is the given fraction to be simplified,
32/3 is the lowest term of 800/75.

Notes: 800/75 simplified in lowest terms
1. 800/75 can be simplified only if the GCF of numerator and denominator is greater than 1. In this case, the GCF of 800 and 75 is 25 which is the greatest factor that evenly divides both numerator and denominator, so this fraction 800/75 can be represented in its reduced form.
2. On the other hand, you can also reduce 800/75 in simplest form by using the factorization method. In this case, the numerator and denominator of fraction should be written in the form of prime factors, so the fraction 800/75 becomes (2 x 2 x 2 x 2 x 2 x 5 x 5)/(3 x 5 x 5). Now you can check and cancel the factors if any factors of numerator and denominator cancel each other to simplify 800/75 in its lowest terms.

step 1 Observe the input parameters and what to be found:
Input values:
Fraction = 800/75

what to be found:
800/75 = ?
Reduce 800/75 in lowest terms.

step 2 Find the prime factors of the numerator of given fraction 800/75.
Prime factors of 800 = 2 x 2 x 2 x 2 x 2 x 5 x 5

step 3 Find the prime factors of the denominator of given fraction 800/75.
Prime factors of 75 = 3 x 5 x 5

step 4 Rewrite the fraction 800/75 in the form of prime factors as like the below:
800/75= (2 x 2 x 2 x 2 x 2 x 5 x 5) / (3 x 5 x 5)

step 5 Check and reduce the factors of 800 and 75 if any factors in the numerator and denominator cancel each other:
= (2 x 2 x 2 x 2 x 2 x 5 x 5) / (3 x 5 x 5)
= (2 x 2 x 2 x 2 x 2 )/(3 )
800/75 = 32/3
Hence,
800/75 in simplest form is 32/3.

800/75 simplified is 32/3, representing fraction in lowest terms is a better way than its original form, to easily recognize the fraction or use in mathematical operations. Simplifying 800/75 to its simplest form involves the greatest common factor or factorization. Recognizing the GCF or prime factors of numerator and denominator of a fraction is key when you start reducing fractions like 800/75 in its lowest terms.