What is 177/413 simplified as a fraction?
177/413 in simplest form is 3/7.
Learn how to find what is 177/413 simplified as a fraction just in a few minutes. We have covered why the GCF or factorization is important to simplify 177/413 in simplest form.
To reduce 177/413 in its lowest terms, you must be familiar with either how to find the greatest common factor or prime factors. Both of these methods are used to recognize if 177/413 can be reduced in simplest form. In this case, the (greatest common factor) GDF of 177 and 413 is 59. Dividing both the numerator and denominator by GCF, the fraction 177/413 becomes 3/7 which is the simplest form.
177/413 Simplified as a Fraction
Using Factorization:
177/413 = (?)
177/413 = (3 x 59)/(7 x 59) write 177/413 in terms of factors
= 3/7
177/413 = 3/7
177/413 simplified is 3/7
Using GCF
177/413 = (?)
GCF of 177 and 413 is 59.
177/413 = (177/59)/(413/59)
= 3/7
177/413 = 3/7
177/413 simplified is 3/7 in fraction form
where,
177/413 is the given fraction to be simplified,
3/7 is the lowest term of 177/413.
Notes: 177/413 simplified in lowest terms
1. 177/413 can be simplified only if the GCF of numerator and denominator is greater than 1. In this case, the GCF of 177 and 413 is 59 which is the greatest factor that evenly divides both numerator and denominator, so this fraction 177/413 can be represented in its reduced form.
2. On the other hand, you can also reduce 177/413 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 177/413 becomes (3 x 59)/(7 x 59). Now you can check and cancel the factors if any factors of numerator and denominator cancel each other to simplify 177/413 in its lowest terms.
step 1 Observe the input parameters and what to be found:
Input values:
Fraction = 177/413
what to be found:
177/413 = ?
Reduce 177/413 in lowest terms.
step 2 Find the prime factors of the numerator of given fraction 177/413.
Prime factors of 177 = 3 x 59
step 3 Find the prime factors of the denominator of given fraction 177/413.
Prime factors of 413 = 7 x 59
step 4 Rewrite the fraction 177/413 in the form of prime factors as like the below:
177/413= (3 x 59) / (7 x 59)
step 5 Check and reduce the factors of 177 and 413 if any factors in the numerator and denominator cancel each other:
= (3 x 59) / (7 x 59)
= (3 )/(7 )
177/413 = 3/7
Hence,
177/413 in simplest form is 3/7.
177/413 simplified is 3/7, representing fraction in lowest terms is a better way than its original form, to easily recognize the fraction or use in mathematical operations. Simplifying 177/413 to its simplest form involves the greatest common factor or factorization. Recognizing the GCF or prime factors of numerator and denominator of a fraction is key when you start reducing fractions like 177/413 in its lowest terms.