GCF of 175/342, 658/231
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 175/342, 658/231 i.e 7/26334 easily. The following is the detailed procedure to determine the greatest common factor of fractions 175/342, 658/231.
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 175/342,658/231?
Given fractions are 175/342,658/231
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 175/342,658/231, numerators are 175,658
Denominators are 342,231
The GCF of 175,658 is 7 .
LCM of 342,231 is 26334.
The greatest common factor of 175/342,658/231 = [GCF of 175,658]/[LCM of 342,231]= 7/26334
Therefore, the GCF of 175/342,658/231 is 7/26334.
To find the highest common factor of 175,658, we have to find the factors of both numbers and list the highest common factor.
The factors of 175 are 1, 5, 7, 25, 35, 175
The factors of 658 are 1, 2, 7, 14, 47, 94, 329, 658
The HCF of 175,658 is 7.
Lets's calculate GCF of 175,658
| 7 | 175, 658 |
| 25, 94 |
∴ So the GCF of the given numbers is 7 = 7
Greatest Common Factor of 175,658 By Matching Biggest Common Factor Method
Now, list down the factors of 175
:1,5,7,25,35,175
Now, list down the factors of 658
:1,2,7,14,47,94,329,658
Greatest Common Factor
We found the factors 175,658 . The biggest common factor number is the GCF number.
So the greatest common factor 175,658 is 7.
Lets's calculate LCM of 342,231
| 3 | 342, 231 |
| 114, 77 |
∴ So the LCM of the given numbers is 3 x 114 x 77 = 26334
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 7/26334
Therefore, the GCF of Fractions 175/342,658/231 is 7/26334
Least Common Multiple of 342,231 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 342,231 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(342,231) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(342,231) x common factors =3 x 1 = 3
LCM(342,231) = ( 342 × 231 ) / 3
LCM(342,231) = 79002 / 3
LCM(342,231) = 26334
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FAQs on GCF of Fractions of 175/342, 658/231
1. What is the HCF of 175,658?
The HCF of 175,658 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 175/342, 658/231?
Answer: GCF of Numerators as per given numbers 175/342, 658/231 is
GCF of Numerators i.e. for 175,658 is 7
LCM of denominators i.e. for 342,231 is 26334.
Thus, GCF of Fractions is 7/26334.Finally, GCF of Fractions for 175/342, 658/231 is 7/26334.