GCF of 234/310, 768/353
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 234/310, 768/353 i.e 6/109430 easily. The following is the detailed procedure to determine the greatest common factor of fractions 234/310, 768/353.
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 234/310,768/353?
Given fractions are 234/310,768/353
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 234/310,768/353, numerators are 234,768
Denominators are 310,353
The GCF of 234,768 is 6 .
LCM of 310,353 is 109430.
The greatest common factor of 234/310,768/353 = [GCF of 234,768]/[LCM of 310,353]= 6/109430
Therefore, the GCF of 234/310,768/353 is 6/109430.
To find the highest common factor of 234,768, we have to find the factors of both numbers and list the highest common factor.
The factors of 234 are 1, 2, 3, 6, 9, 13, 18, 26, 39, 78, 117, 234
The factors of 768 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 256, 384, 768
The HCF of 234,768 is 6.
Lets's calculate GCF of 234,768
| 2 | 234, 768 |
| 3 | 117, 384 |
| 39, 128 |
∴ So the GCF of the given numbers is 2 x 3 = 6
Greatest Common Factor of 234,768 By Matching Biggest Common Factor Method
Now, list down the factors of 234
:1,2,3,6,9,13,18,26,39,78,117,234
Now, list down the factors of 768
:1,2,3,4,6,8,12,16,24,32,48,64,96,128,192,256,384,768
Greatest Common Factor
We found the factors 234,768 . The biggest common factor number is the GCF number.
So the greatest common factor 234,768 is 6.
Lets's calculate LCM of 310,353
Given numbers has no common factors except 1. So, there LCM is their product i.e 109430
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/109430
Therefore, the GCF of Fractions 234/310,768/353 is 6/109430
Least Common Multiple of 310,353 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 310,353 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(310,353) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(310,353) x common factors =1 x 1 = 1
LCM(310,353) = ( 310 × 353 ) / 1
LCM(310,353) = 109430 / 1
LCM(310,353) = 109430
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FAQs on GCF of Fractions of 234/310, 768/353
1. What is the HCF of 234,768?
The HCF of 234,768 is 6
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 234/310, 768/353?
Answer: GCF of Numerators as per given numbers 234/310, 768/353 is
GCF of Numerators i.e. for 234,768 is 6
LCM of denominators i.e. for 310,353 is 109430.
Thus, GCF of Fractions is 6/109430.Finally, GCF of Fractions for 234/310, 768/353 is 6/109430.