180/465 Simplified

Learn how to find what is 180/465 simplified as a fraction just in a few minutes. We have covered why the GCF or factorization is important to simplify 180/465 in simplest form.

To reduce 180/465 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 180/465 can be reduced in simplest form. In this case, the (greatest common factor) GDF of 180 and 465 is 15. Dividing both the numerator and denominator by GCF, the fraction 180/465 becomes 12/31 which is the simplest form.

180/465 Simplified as a Fraction
Using Factorization:
180/465 = (?)
180/465 = (2 x 2 x 3 x 3 x 5)/(3 x 5 x 31)      write 180/465 in terms of factors
= 12/31
180/465 = 12/31
180/465 simplified is 12/31

Using GCF
180/465 = (?)
GCF of 180 and 465 is 15.
180/465 = (180/15)/(465/15)
= 12/31
180/465 = 12/31
180/465 simplified is 12/31 in fraction form
where,
180/465 is the given fraction to be simplified,
12/31 is the lowest term of 180/465.

Notes: 180/465 simplified in lowest terms
1. 180/465 can be simplified only if the GCF of numerator and denominator is greater than 1. In this case, the GCF of 180 and 465 is 15 which is the greatest factor that evenly divides both numerator and denominator, so this fraction 180/465 can be represented in its reduced form.
2. On the other hand, you can also reduce 180/465 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 180/465 becomes (2 x 2 x 3 x 3 x 5)/(3 x 5 x 31). Now you can check and cancel the factors if any factors of numerator and denominator cancel each other to simplify 180/465 in its lowest terms.

step 1 Observe the input parameters and what to be found:
Input values:
Fraction = 180/465

what to be found:
180/465 = ?
Reduce 180/465 in lowest terms.

step 2 Find the prime factors of the numerator of given fraction 180/465.
Prime factors of 180 = 2 x 2 x 3 x 3 x 5

step 3 Find the prime factors of the denominator of given fraction 180/465.
Prime factors of 465 = 3 x 5 x 31

step 4 Rewrite the fraction 180/465 in the form of prime factors as like the below:
180/465= (2 x 2 x 3 x 3 x 5) / (3 x 5 x 31)

step 5 Check and reduce the factors of 180 and 465 if any factors in the numerator and denominator cancel each other:
= (2 x 2 x 3 x 3 x 5) / (3 x 5 x 31)
= (2 x 2 x 3 )/( 31)
180/465 = 12/31
Hence,
180/465 in simplest form is 12/31.

180/465 simplified is 12/31, representing fraction in lowest terms is a better way than its original form, to easily recognize the fraction or use in mathematical operations. Simplifying 180/465 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 180/465 in its lowest terms.