825/970 Simplified

Learn how to find what is 825/970 simplified as a fraction just in a few minutes. We have covered why the greatest common divisor or factorization is important to simplify 825/970 in simplest form.

To simplify 825/970 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 825/970 can be reduced in simplest form. In this case, the greatest common divisor of 825 and 970 is 5. Dividing both the numerator and denominator by GCD, the fraction 825/970 becomes 165/194 which is the simplest form.

Simplify 825/970 as a Fraction
Using Factorization:
825/970 = (?)
825/970 = (3 x 5 x 5 x 11)/(2 x 5 x 97)      //write 825/970 in terms of factors
= 165/194
825/970 = 165/194
825/970 simplified is 165/194

Using GCD:
825/970 = (?)
GCD of 825 and 970 is 5.
825/970 = (825/5)/(970/5)
= 165/194
825/970 = 165/194
825/970 simplified is 165/194 in fraction form
where,
825/970 is the given fraction to be simplified,
165/194 is the lowest term of 825/970.

Notes: Simplify 825/970 in lowest terms
1. 825/970 can be simplified only if the GCD of numerator and denominator is greater than 1. In this case, the GCD of 825 and 970 is 5 which is the greatest factor that evenly divides both numerator and denominator, so this fraction 825/970 can be represented in its reduced form.
2. On the other hand, you can also reduce 825/970 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 825/970 becomes (3 x 5 x 5 x 11)/(2 x 5 x 97). Now you can check and cancel the factors if any factors of numerator and denominator cancel each other to simplify 825/970 in its lowest terms.

step 1 Observe the input parameters and what to be found:
Input values:
Fraction = 825/970

what to be found:
825/970 = ?
Simplify 825/970 in lowest terms.

step 2 Find the prime factors of the numerator of given fraction 825/970.
Prime factors of 825 = 3 x 5 x 5 x 11

step 3 Find the prime factors of the denominator of given fraction 825/970.
Prime factors of 970 = 2 x 5 x 97

step 4 Rewrite the fraction 825/970 in the form of prime factors as like the below:
825/970= (3 x 5 x 5 x 11) / (2 x 5 x 97)

step 5 Check and reduce the factors of 825 and 970 if any factors in the numerator and denominator cancel each other:
= (3 x 5 x 5 x 11) / (2 x 5 x 97)
= (3 x 5 x 11)/(2 x 97)
825/970 = 165/194

Hence,
825/970 in simplest form is 165/194.

Representing fraction 825/970 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 825/970 in its lowest terms.