105/840 Simplified

Learn how to find what is 105/840 simplified as a fraction just in a few minutes. We have covered why the greatest common divisor or factorization is important to simplify 105/840 in simplest form.

To simplify 105/840 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 105/840 can be reduced in simplest form. In this case, the greatest common divisor of 105 and 840 is 105. Dividing both the numerator and denominator by GCD, the fraction 105/840 becomes 1/8 which is the simplest form.

Simplify 105/840 as a Fraction
Using Factorization:
105/840 = (?)
105/840 = (3 x 5 x 7)/(2 x 2 x 2 x 3 x 5 x 7)      //write 105/840 in terms of factors
= 1/8
105/840 = 1/8
105/840 simplified is 1/8

Using GCD:
105/840 = (?)
GCD of 105 and 840 is 105.
105/840 = (105/105)/(840/105)
= 1/8
105/840 = 1/8
105/840 simplified is 1/8 in fraction form
where,
105/840 is the given fraction to be simplified,
1/8 is the lowest term of 105/840.

Notes: Simplify 105/840 in lowest terms
1. 105/840 can be simplified only if the GCD of numerator and denominator is greater than 1. In this case, the GCD of 105 and 840 is 105 which is the greatest factor that evenly divides both numerator and denominator, so this fraction 105/840 can be represented in its reduced form.
2. On the other hand, you can also reduce 105/840 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 105/840 becomes (3 x 5 x 7)/(2 x 2 x 2 x 3 x 5 x 7). Now you can check and cancel the factors if any factors of numerator and denominator cancel each other to simplify 105/840 in its lowest terms.

step 1 Observe the input parameters and what to be found:
Input values:
Fraction = 105/840

what to be found:
105/840 = ?
Simplify 105/840 in lowest terms.

step 2 Find the prime factors of the numerator of given fraction 105/840.
Prime factors of 105 = 3 x 5 x 7

step 3 Find the prime factors of the denominator of given fraction 105/840.
Prime factors of 840 = 2 x 2 x 2 x 3 x 5 x 7

step 4 Rewrite the fraction 105/840 in the form of prime factors as like the below:
105/840= (3 x 5 x 7) / (2 x 2 x 2 x 3 x 5 x 7)

step 5 Check and reduce the factors of 105 and 840 if any factors in the numerator and denominator cancel each other:
= (3 x 5 x 7) / (2 x 2 x 2 x 3 x 5 x 7)
= (1)/(2 x 2 x 2 )
105/840 = 1/8

Hence,
105/840 in simplest form is 1/8.

Representing fraction 105/840 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 105/840 in its lowest terms.