725/45 Simplified

Learn how to find what is 725/45 simplified as a fraction just in a few minutes. We have covered why the GCF or factorization is important to simplify 725/45 in simplest form.

To reduce 725/45 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 725/45 can be reduced in simplest form. In this case, the (greatest common factor) GDF of 725 and 45 is 5. Dividing both the numerator and denominator by GCF, the fraction 725/45 becomes 145/9 which is the simplest form.

725/45 Simplified as a Fraction
Using Factorization:
725/45 = (?)
725/45 = (5 x 5 x 29)/(3 x 3 x 5)      write 725/45 in terms of factors
= 145/9
725/45 = 145/9
725/45 simplified is 145/9

Using GCF
725/45 = (?)
GCF of 725 and 45 is 5.
725/45 = (725/5)/(45/5)
= 145/9
725/45 = 145/9
725/45 simplified is 145/9 in fraction form
where,
725/45 is the given fraction to be simplified,
145/9 is the lowest term of 725/45.

Notes: 725/45 simplified in lowest terms
1. 725/45 can be simplified only if the GCF of numerator and denominator is greater than 1. In this case, the GCF of 725 and 45 is 5 which is the greatest factor that evenly divides both numerator and denominator, so this fraction 725/45 can be represented in its reduced form.
2. On the other hand, you can also reduce 725/45 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 725/45 becomes (5 x 5 x 29)/(3 x 3 x 5). Now you can check and cancel the factors if any factors of numerator and denominator cancel each other to simplify 725/45 in its lowest terms.

step 1 Observe the input parameters and what to be found:
Input values:
Fraction = 725/45

what to be found:
725/45 = ?
Reduce 725/45 in lowest terms.

step 2 Find the prime factors of the numerator of given fraction 725/45.
Prime factors of 725 = 5 x 5 x 29

step 3 Find the prime factors of the denominator of given fraction 725/45.
Prime factors of 45 = 3 x 3 x 5

step 4 Rewrite the fraction 725/45 in the form of prime factors as like the below:
725/45= (5 x 5 x 29) / (3 x 3 x 5)

step 5 Check and reduce the factors of 725 and 45 if any factors in the numerator and denominator cancel each other:
= (5 x 5 x 29) / (3 x 3 x 5)
= ( 5 x 29)/(3 x 3 )
725/45 = 145/9
Hence,
725/45 in simplest form is 145/9.

725/45 simplified is 145/9, representing fraction in lowest terms is a better way than its original form, to easily recognize the fraction or use in mathematical operations. Simplifying 725/45 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 725/45 in its lowest terms.