40/172 Simplified

Learn how to find what is 40/172 simplified as a fraction just in a few minutes. We have covered why the greatest common divisor or factorization is important to simplify 40/172 in simplest form.

To simplify 40/172 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 40/172 can be reduced in simplest form. In this case, the greatest common divisor of 40 and 172 is 4. Dividing both the numerator and denominator by GCD, the fraction 40/172 becomes 10/43 which is the simplest form.

Simplify 40/172 as a Fraction
Using Factorization:
40/172 = (?)
40/172 = (2 x 2 x 2 x 5)/(2 x 2 x 43)      //write 40/172 in terms of factors
= 10/43
40/172 = 10/43
40/172 simplified is 10/43

Using GCD:
40/172 = (?)
GCD of 40 and 172 is 4.
40/172 = (40/4)/(172/4)
= 10/43
40/172 = 10/43
40/172 simplified is 10/43 in fraction form
where,
40/172 is the given fraction to be simplified,
10/43 is the lowest term of 40/172.

Notes: Simplify 40/172 in lowest terms
1. 40/172 can be simplified only if the GCD of numerator and denominator is greater than 1. In this case, the GCD of 40 and 172 is 4 which is the greatest factor that evenly divides both numerator and denominator, so this fraction 40/172 can be represented in its reduced form.
2. On the other hand, you can also reduce 40/172 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 40/172 becomes (2 x 2 x 2 x 5)/(2 x 2 x 43). Now you can check and cancel the factors if any factors of numerator and denominator cancel each other to simplify 40/172 in its lowest terms.

step 1 Observe the input parameters and what to be found:
Input values:
Fraction = 40/172

what to be found:
40/172 = ?
Simplify 40/172 in lowest terms.

step 2 Find the prime factors of the numerator of given fraction 40/172.
Prime factors of 40 = 2 x 2 x 2 x 5

step 3 Find the prime factors of the denominator of given fraction 40/172.
Prime factors of 172 = 2 x 2 x 43

step 4 Rewrite the fraction 40/172 in the form of prime factors as like the below:
40/172= (2 x 2 x 2 x 5) / (2 x 2 x 43)

step 5 Check and reduce the factors of 40 and 172 if any factors in the numerator and denominator cancel each other:
= (2 x 2 x 2 x 5) / (2 x 2 x 43)
= ( 2 x 5)/( 43)
40/172 = 10/43

Hence,
40/172 in simplest form is 10/43.

Representing fraction 40/172 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 40/172 in its lowest terms.