GCF of 617/34, 178/118
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 617/34, 178/118 i.e 1/2006 easily. The following is the detailed procedure to determine the greatest common factor of fractions 617/34, 178/118.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
What is the GCF of 617/34,178/118?
Given fractions are 617/34,178/118
To find the GCF of fractions, we have to find the GCF of numerator numbers and LCM of denominator numbers. Its formula is given by
GCF of Fraction = Greatest Common Factor of Numerator/Least Common Multiple of Denominators
In the fractions 617/34,178/118, numerators are 617,178
Denominators are 34,118
The GCF of 617,178 is 1 .
LCM of 34,118 is 2006.
The greatest common factor of 617/34,178/118 = [GCF of 617,178]/[LCM of 34,118]= 1/2006
Therefore, the GCF of 617/34,178/118 is 1/2006.
To find the highest common factor of 617,178, we have to find the factors of both numbers and list the highest common factor.
The factors of 617 are 1, 617
The factors of 178 are 1, 2, 89, 178
The HCF of 617,178 is 1.
Lets's calculate GCF of 617,178
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 617,178 By Matching Biggest Common Factor Method
Now, list down the factors of 617
:1,617
Now, list down the factors of 178
:1,2,89,178
Greatest Common Factor
We found the factors 617,178 . The biggest common factor number is the GCF number.
So the greatest common factor 617,178 is 1.
Lets's calculate LCM of 34,118
| 2 | 34, 118 |
| 17, 59 |
∴ So the LCM of the given numbers is 2 x 17 x 59 = 2006
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/2006
Therefore, the GCF of Fractions 617/34,178/118 is 1/2006
Least Common Multiple of 34,118 with GCF Formula
The formula of LCM is LCM(a1,a2,a3....,an) = ( a1 × a2 × a3 × .... × an) / GCF(a1,a2,a3....,an) x common factors(if more than 2 numbers have common factors).
We need to calculate greatest common factor of 34,118 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(34,118) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(34,118) x common factors =2 x 1 = 2
LCM(34,118) = ( 34 × 118 ) / 2
LCM(34,118) = 4012 / 2
LCM(34,118) = 2006
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FAQs on GCF of Fractions of 617/34, 178/118
1. What is the HCF of 617,178?
The HCF of 617,178 is 1
2. What is the GCF of a fraction?
The GCF of a fraction is defined as the greatest fraction that divides exactly into 2 or more fractions.
3. How to find GCF in Fractions?
Answer: GCF of fractions can be found using the simple formula GCF of Fractions = GCF of Numerators/LCM of Denominators.
4. What is the GCF of Fractions for 617/34, 178/118?
Answer: GCF of Numerators as per given numbers 617/34, 178/118 is
GCF of Numerators i.e. for 617,178 is 1
LCM of denominators i.e. for 34,118 is 2006.
Thus, GCF of Fractions is 1/2006.Finally, GCF of Fractions for 617/34, 178/118 is 1/2006.