GCF of 354/320, 535/344
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 354/320, 535/344 i.e 1/13760 easily. The following is the detailed procedure to determine the greatest common factor of fractions 354/320, 535/344.
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 354/320,535/344?
Given fractions are 354/320,535/344
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 354/320,535/344, numerators are 354,535
Denominators are 320,344
The GCF of 354,535 is 1 .
LCM of 320,344 is 13760.
The greatest common factor of 354/320,535/344 = [GCF of 354,535]/[LCM of 320,344]= 1/13760
Therefore, the GCF of 354/320,535/344 is 1/13760.
To find the highest common factor of 354,535, we have to find the factors of both numbers and list the highest common factor.
The factors of 354 are 1, 2, 3, 6, 59, 118, 177, 354
The factors of 535 are 1, 5, 107, 535
The HCF of 354,535 is 1.
Lets's calculate GCF of 354,535
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 354,535 By Matching Biggest Common Factor Method
Now, list down the factors of 354
:1,2,3,6,59,118,177,354
Now, list down the factors of 535
:1,5,107,535
Greatest Common Factor
We found the factors 354,535 . The biggest common factor number is the GCF number.
So the greatest common factor 354,535 is 1.
Lets's calculate LCM of 320,344
| 2 | 320, 344 |
| 2 | 160, 172 |
| 2 | 80, 86 |
| 40, 43 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 40 x 43 = 13760
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/13760
Therefore, the GCF of Fractions 354/320,535/344 is 1/13760
Least Common Multiple of 320,344 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 320,344 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(320,344) = 8
common factors(in case of two or more numbers have common factors) = 1
GCF(320,344) x common factors =8 x 1 = 8
LCM(320,344) = ( 320 × 344 ) / 8
LCM(320,344) = 110080 / 8
LCM(320,344) = 13760
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FAQs on GCF of Fractions of 354/320, 535/344
1. What is the HCF of 354,535?
The HCF of 354,535 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 354/320, 535/344?
Answer: GCF of Numerators as per given numbers 354/320, 535/344 is
GCF of Numerators i.e. for 354,535 is 1
LCM of denominators i.e. for 320,344 is 13760.
Thus, GCF of Fractions is 1/13760.Finally, GCF of Fractions for 354/320, 535/344 is 1/13760.