165/40 Simplified

Learn how to find what is 165/40 simplified as a fraction just in a few minutes. We have covered why the GCF or factorization is important to simplify 165/40 in simplest form.

To reduce 165/40 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 165/40 can be reduced in simplest form. In this case, the (greatest common factor) GDF of 165 and 40 is 5. Dividing both the numerator and denominator by GCF, the fraction 165/40 becomes 33/8 which is the simplest form.

165/40 Simplified as a Fraction
Using Factorization:
165/40 = (?)
165/40 = (3 x 5 x 11)/(2 x 2 x 2 x 5)      write 165/40 in terms of factors
= 33/8
165/40 = 33/8
165/40 simplified is 33/8

Using GCF
165/40 = (?)
GCF of 165 and 40 is 5.
165/40 = (165/5)/(40/5)
= 33/8
165/40 = 33/8
165/40 simplified is 33/8 in fraction form
where,
165/40 is the given fraction to be simplified,
33/8 is the lowest term of 165/40.

Notes: 165/40 simplified in lowest terms
1. 165/40 can be simplified only if the GCF of numerator and denominator is greater than 1. In this case, the GCF of 165 and 40 is 5 which is the greatest factor that evenly divides both numerator and denominator, so this fraction 165/40 can be represented in its reduced form.
2. On the other hand, you can also reduce 165/40 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 165/40 becomes (3 x 5 x 11)/(2 x 2 x 2 x 5). Now you can check and cancel the factors if any factors of numerator and denominator cancel each other to simplify 165/40 in its lowest terms.

step 1 Observe the input parameters and what to be found:
Input values:
Fraction = 165/40

what to be found:
165/40 = ?
Reduce 165/40 in lowest terms.

step 2 Find the prime factors of the numerator of given fraction 165/40.
Prime factors of 165 = 3 x 5 x 11

step 3 Find the prime factors of the denominator of given fraction 165/40.
Prime factors of 40 = 2 x 2 x 2 x 5

step 4 Rewrite the fraction 165/40 in the form of prime factors as like the below:
165/40= (3 x 5 x 11) / (2 x 2 x 2 x 5)

step 5 Check and reduce the factors of 165 and 40 if any factors in the numerator and denominator cancel each other:
= (3 x 5 x 11) / (2 x 2 x 2 x 5)
= (3 x 11)/(2 x 2 x 2 )
165/40 = 33/8
Hence,
165/40 in simplest form is 33/8.

165/40 simplified is 33/8, representing fraction in lowest terms is a better way than its original form, to easily recognize the fraction or use in mathematical operations. Simplifying 165/40 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 165/40 in its lowest terms.