780/9900 Simplified

Learn how to find what is 780/9900 simplified as a fraction just in a few minutes. We have covered why the greatest common divisor or factorization is important to simplify 780/9900 in simplest form.

To simplify 780/9900 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 780/9900 can be reduced in simplest form. In this case, the greatest common divisor of 780 and 9900 is 60. Dividing both the numerator and denominator by GCD, the fraction 780/9900 becomes 13/165 which is the simplest form.

Simplify 780/9900 as a Fraction
Using Factorization:
780/9900 = (?)
780/9900 = (2 x 2 x 3 x 5 x 13)/(2 x 2 x 3 x 3 x 5 x 5 x 11)      //write 780/9900 in terms of factors
= 13/165
780/9900 = 13/165
780/9900 simplified is 13/165

Using GCD:
780/9900 = (?)
GCD of 780 and 9900 is 60.
780/9900 = (780/60)/(9900/60)
= 13/165
780/9900 = 13/165
780/9900 simplified is 13/165 in fraction form
where,
780/9900 is the given fraction to be simplified,
13/165 is the lowest term of 780/9900.

Notes: Simplify 780/9900 in lowest terms
1. 780/9900 can be simplified only if the GCD of numerator and denominator is greater than 1. In this case, the GCD of 780 and 9900 is 60 which is the greatest factor that evenly divides both numerator and denominator, so this fraction 780/9900 can be represented in its reduced form.
2. On the other hand, you can also reduce 780/9900 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 780/9900 becomes (2 x 2 x 3 x 5 x 13)/(2 x 2 x 3 x 3 x 5 x 5 x 11). Now you can check and cancel the factors if any factors of numerator and denominator cancel each other to simplify 780/9900 in its lowest terms.

step 1 Observe the input parameters and what to be found:
Input values:
Fraction = 780/9900

what to be found:
780/9900 = ?
Simplify 780/9900 in lowest terms.

step 2 Find the prime factors of the numerator of given fraction 780/9900.
Prime factors of 780 = 2 x 2 x 3 x 5 x 13

step 3 Find the prime factors of the denominator of given fraction 780/9900.
Prime factors of 9900 = 2 x 2 x 3 x 3 x 5 x 5 x 11

step 4 Rewrite the fraction 780/9900 in the form of prime factors as like the below:
780/9900= (2 x 2 x 3 x 5 x 13) / (2 x 2 x 3 x 3 x 5 x 5 x 11)

step 5 Check and reduce the factors of 780 and 9900 if any factors in the numerator and denominator cancel each other:
= (2 x 2 x 3 x 5 x 13) / (2 x 2 x 3 x 3 x 5 x 5 x 11)
= ( 13)/( 3 x 5 x 11)
780/9900 = 13/165

Hence,
780/9900 in simplest form is 13/165.

Representing fraction 780/9900 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 780/9900 in its lowest terms.