49/343 Simplified

Learn how to find what is 49/343 simplified as a fraction just in a few minutes. We have covered why the GCF or factorization is important to simplify 49/343 in simplest form.

To reduce 49/343 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 49/343 can be reduced in simplest form. In this case, the (greatest common factor) GDF of 49 and 343 is 49. Dividing both the numerator and denominator by GCF, the fraction 49/343 becomes 1/7 which is the simplest form.

49/343 Simplified as a Fraction
Using Factorization:
49/343 = (?)
49/343 = (7 x 7)/(7 x 7 x 7)      write 49/343 in terms of factors
= 1/7
49/343 = 1/7
49/343 simplified is 1/7

Using GCF
49/343 = (?)
GCF of 49 and 343 is 49.
49/343 = (49/49)/(343/49)
= 1/7
49/343 = 1/7
49/343 simplified is 1/7 in fraction form
where,
49/343 is the given fraction to be simplified,
1/7 is the lowest term of 49/343.

Notes: 49/343 simplified in lowest terms
1. 49/343 can be simplified only if the GCF of numerator and denominator is greater than 1. In this case, the GCF of 49 and 343 is 49 which is the greatest factor that evenly divides both numerator and denominator, so this fraction 49/343 can be represented in its reduced form.
2. On the other hand, you can also reduce 49/343 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 49/343 becomes (7 x 7)/(7 x 7 x 7). Now you can check and cancel the factors if any factors of numerator and denominator cancel each other to simplify 49/343 in its lowest terms.

step 1 Observe the input parameters and what to be found:
Input values:
Fraction = 49/343

what to be found:
49/343 = ?
Reduce 49/343 in lowest terms.

step 2 Find the prime factors of the numerator of given fraction 49/343.
Prime factors of 49 = 7 x 7

step 3 Find the prime factors of the denominator of given fraction 49/343.
Prime factors of 343 = 7 x 7 x 7

step 4 Rewrite the fraction 49/343 in the form of prime factors as like the below:
49/343= (7 x 7) / (7 x 7 x 7)

step 5 Check and reduce the factors of 49 and 343 if any factors in the numerator and denominator cancel each other:
= (7 x 7) / (7 x 7 x 7)
= (1)/( 7)
49/343 = 1/7
Hence,
49/343 in simplest form is 1/7.

49/343 simplified is 1/7, representing fraction in lowest terms is a better way than its original form, to easily recognize the fraction or use in mathematical operations. Simplifying 49/343 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 49/343 in its lowest terms.