105/972 Simplified

Learn how to find what is 105/972 simplified as a fraction just in a few minutes. We have covered why the greatest common divisor or factorization is important to simplify 105/972 in simplest form.

To simplify 105/972 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 105/972 can be reduced in simplest form. In this case, the greatest common divisor of 105 and 972 is 3. Dividing both the numerator and denominator by GCD, the fraction 105/972 becomes 35/324 which is the simplest form.

Simplify 105/972 as a Fraction
Using Factorization:
105/972 = (?)
105/972 = (3 x 5 x 7)/(2 x 2 x 3 x 3 x 3 x 3 x 3)      //write 105/972 in terms of factors
= 35/324
105/972 = 35/324
105/972 simplified is 35/324

Using GCD:
105/972 = (?)
GCD of 105 and 972 is 3.
105/972 = (105/3)/(972/3)
= 35/324
105/972 = 35/324
105/972 simplified is 35/324 in fraction form
where,
105/972 is the given fraction to be simplified,
35/324 is the lowest term of 105/972.

Notes: Simplify 105/972 in lowest terms
1. 105/972 can be simplified only if the GCD of numerator and denominator is greater than 1. In this case, the GCD of 105 and 972 is 3 which is the greatest factor that evenly divides both numerator and denominator, so this fraction 105/972 can be represented in its reduced form.
2. On the other hand, you can also reduce 105/972 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 105/972 becomes (3 x 5 x 7)/(2 x 2 x 3 x 3 x 3 x 3 x 3). Now you can check and cancel the factors if any factors of numerator and denominator cancel each other to simplify 105/972 in its lowest terms.

step 1 Observe the input parameters and what to be found:
Input values:
Fraction = 105/972

what to be found:
105/972 = ?
Simplify 105/972 in lowest terms.

step 2 Find the prime factors of the numerator of given fraction 105/972.
Prime factors of 105 = 3 x 5 x 7

step 3 Find the prime factors of the denominator of given fraction 105/972.
Prime factors of 972 = 2 x 2 x 3 x 3 x 3 x 3 x 3

step 4 Rewrite the fraction 105/972 in the form of prime factors as like the below:
105/972= (3 x 5 x 7) / (2 x 2 x 3 x 3 x 3 x 3 x 3)

step 5 Check and reduce the factors of 105 and 972 if any factors in the numerator and denominator cancel each other:
= (3 x 5 x 7) / (2 x 2 x 3 x 3 x 3 x 3 x 3)
= ( 5 x 7)/(2 x 2 x 3 x 3 x 3 x 3)
105/972 = 35/324

Hence,
105/972 in simplest form is 35/324.

Representing fraction 105/972 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 105/972 in its lowest terms.