69/360 Simplified

Learn how to find what is 69/360 simplified as a fraction just in a few minutes. We have covered why the greatest common divisor or factorization is important to simplify 69/360 in simplest form.

To simplify 69/360 in its lowest terms, you must be familiar with either how to find the greatest common divisor or prime factors. Both of these methods are used to recognize if 69/360 can be reduced in simplest form. In this case, the greatest common divisor of 69 and 360 is 3. Dividing both the numerator and denominator by GCD, the fraction 69/360 becomes 23/120 which is the simplest form.

Simplify 69/360 as a Fraction
Using Factorization:
69/360 = (?)
69/360 = (3 x 23)/(2 x 2 x 2 x 3 x 3 x 5)      //write 69/360 in terms of factors
= 23/120
69/360 = 23/120
69/360 simplified is 23/120

Using GCD:
69/360 = (?)
GCD of 69 and 360 is 3.
69/360 = (69/3)/(360/3)
= 23/120
69/360 = 23/120
69/360 simplified is 23/120 in fraction form
where,
69/360 is the given fraction to be simplified,
23/120 is the lowest term of 69/360.

Notes: Simplify 69/360 in lowest terms
1. 69/360 can be simplified only if the GCD of numerator and denominator is greater than 1. In this case, the GCD of 69 and 360 is 3 which is the greatest factor that evenly divides both numerator and denominator, so this fraction 69/360 can be represented in its reduced form.
2. On the other hand, you can also reduce 69/360 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 69/360 becomes (3 x 23)/(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 69/360 in its lowest terms.

step 1 Observe the input parameters and what to be found:
Input values:
Fraction = 69/360

what to be found:
69/360 = ?
Simplify 69/360 in lowest terms.

step 2 Find the prime factors of the numerator of given fraction 69/360.
Prime factors of 69 = 3 x 23

step 3 Find the prime factors of the denominator of given fraction 69/360.
Prime factors of 360 = 2 x 2 x 2 x 3 x 3 x 5

step 4 Rewrite the fraction 69/360 in the form of prime factors as like the below:
69/360= (3 x 23) / (2 x 2 x 2 x 3 x 3 x 5)

step 5 Check and reduce the factors of 69 and 360 if any factors in the numerator and denominator cancel each other:
= (3 x 23) / (2 x 2 x 2 x 3 x 3 x 5)
= ( 23)/(2 x 2 x 2 x 3 x 5)
69/360 = 23/120

Hence,
69/360 in simplest form is 23/120.

Representing fraction 69/360 in lowest terms is a better way than its original form to easily recognize the fraction or use in mathematical operations. Simplify fraction involves finding the greatest common factor or factorization. Recognizing the GCD or prime factors of numerator and denominator of a fraction is key when you start reducing fractions like 69/360 in its lowest terms.