872/360 Simplified

Learn how to find what is 872/360 simplified as a fraction just in a few minutes. We have covered why the GCF or factorization is important to simplify 872/360 in simplest form.

To reduce 872/360 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 872/360 can be reduced in simplest form. In this case, the (greatest common factor) GDF of 872 and 360 is 8. Dividing both the numerator and denominator by GCF, the fraction 872/360 becomes 109/45 which is the simplest form.

872/360 Simplified as a Fraction
Using Factorization:
872/360 = (?)
872/360 = (2 x 2 x 2 x 109)/(2 x 2 x 2 x 3 x 3 x 5)      write 872/360 in terms of factors
= 109/45
872/360 = 109/45
872/360 simplified is 109/45

Using GCF
872/360 = (?)
GCF of 872 and 360 is 8.
872/360 = (872/8)/(360/8)
= 109/45
872/360 = 109/45
872/360 simplified is 109/45 in fraction form
where,
872/360 is the given fraction to be simplified,
109/45 is the lowest term of 872/360.

Notes: 872/360 simplified in lowest terms
1. 872/360 can be simplified only if the GCF of numerator and denominator is greater than 1. In this case, the GCF of 872 and 360 is 8 which is the greatest factor that evenly divides both numerator and denominator, so this fraction 872/360 can be represented in its reduced form.
2. On the other hand, you can also reduce 872/360 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 872/360 becomes (2 x 2 x 2 x 109)/(2 x 2 x 2 x 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 872/360 in its lowest terms.

step 1 Observe the input parameters and what to be found:
Input values:
Fraction = 872/360

what to be found:
872/360 = ?
Reduce 872/360 in lowest terms.

step 2 Find the prime factors of the numerator of given fraction 872/360.
Prime factors of 872 = 2 x 2 x 2 x 109

step 3 Find the prime factors of the denominator of given fraction 872/360.
Prime factors of 360 = 2 x 2 x 2 x 3 x 3 x 5

step 4 Rewrite the fraction 872/360 in the form of prime factors as like the below:
872/360= (2 x 2 x 2 x 109) / (2 x 2 x 2 x 3 x 3 x 5)

step 5 Check and reduce the factors of 872 and 360 if any factors in the numerator and denominator cancel each other:
= (2 x 2 x 2 x 109) / (2 x 2 x 2 x 3 x 3 x 5)
= ( 109)/( 3 x 3 x 5)
872/360 = 109/45
Hence,
872/360 in simplest form is 109/45.

872/360 simplified is 109/45, representing fraction in lowest terms is a better way than its original form, to easily recognize the fraction or use in mathematical operations. Simplifying 872/360 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 872/360 in its lowest terms.