GCF of 231/854, 217/278
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 231/854, 217/278 i.e 7/118706 easily. The following is the detailed procedure to determine the greatest common factor of fractions 231/854, 217/278.
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 231/854,217/278?
Given fractions are 231/854,217/278
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 231/854,217/278, numerators are 231,217
Denominators are 854,278
The GCF of 231,217 is 7 .
LCM of 854,278 is 118706.
The greatest common factor of 231/854,217/278 = [GCF of 231,217]/[LCM of 854,278]= 7/118706
Therefore, the GCF of 231/854,217/278 is 7/118706.
To find the highest common factor of 231,217, we have to find the factors of both numbers and list the highest common factor.
The factors of 231 are 1, 3, 7, 11, 21, 33, 77, 231
The factors of 217 are 1, 7, 31, 217
The HCF of 231,217 is 7.
Lets's calculate GCF of 231,217
| 7 | 231, 217 |
| 33, 31 |
∴ So the GCF of the given numbers is 7 = 7
Greatest Common Factor of 231,217 By Matching Biggest Common Factor Method
Now, list down the factors of 231
:1,3,7,11,21,33,77,231
Now, list down the factors of 217
:1,7,31,217
Greatest Common Factor
We found the factors 231,217 . The biggest common factor number is the GCF number.
So the greatest common factor 231,217 is 7.
Lets's calculate LCM of 854,278
| 2 | 854, 278 |
| 427, 139 |
∴ So the LCM of the given numbers is 2 x 427 x 139 = 118706
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 7/118706
Therefore, the GCF of Fractions 231/854,217/278 is 7/118706
Least Common Multiple of 854,278 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 854,278 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(854,278) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(854,278) x common factors =2 x 1 = 2
LCM(854,278) = ( 854 × 278 ) / 2
LCM(854,278) = 237412 / 2
LCM(854,278) = 118706
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FAQs on GCF of Fractions of 231/854, 217/278
1. What is the HCF of 231,217?
The HCF of 231,217 is 7
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 231/854, 217/278?
Answer: GCF of Numerators as per given numbers 231/854, 217/278 is
GCF of Numerators i.e. for 231,217 is 7
LCM of denominators i.e. for 854,278 is 118706.
Thus, GCF of Fractions is 7/118706.Finally, GCF of Fractions for 231/854, 217/278 is 7/118706.