GCF of 176/231, 342/305
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 176/231, 342/305 i.e 2/70455 easily. The following is the detailed procedure to determine the greatest common factor of fractions 176/231, 342/305.
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 176/231,342/305?
Given fractions are 176/231,342/305
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 176/231,342/305, numerators are 176,342
Denominators are 231,305
The GCF of 176,342 is 2 .
LCM of 231,305 is 70455.
The greatest common factor of 176/231,342/305 = [GCF of 176,342]/[LCM of 231,305]= 2/70455
Therefore, the GCF of 176/231,342/305 is 2/70455.
To find the highest common factor of 176,342, we have to find the factors of both numbers and list the highest common factor.
The factors of 176 are 1, 2, 4, 8, 11, 16, 22, 44, 88, 176
The factors of 342 are 1, 2, 3, 6, 9, 18, 19, 38, 57, 114, 171, 342
The HCF of 176,342 is 2.
Lets's calculate GCF of 176,342
| 2 | 176, 342 |
| 88, 171 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 176,342 By Matching Biggest Common Factor Method
Now, list down the factors of 176
:1,2,4,8,11,16,22,44,88,176
Now, list down the factors of 342
:1,2,3,6,9,18,19,38,57,114,171,342
Greatest Common Factor
We found the factors 176,342 . The biggest common factor number is the GCF number.
So the greatest common factor 176,342 is 2.
Lets's calculate LCM of 231,305
Given numbers has no common factors except 1. So, there LCM is their product i.e 70455
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/70455
Therefore, the GCF of Fractions 176/231,342/305 is 2/70455
Least Common Multiple of 231,305 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 231,305 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(231,305) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(231,305) x common factors =1 x 1 = 1
LCM(231,305) = ( 231 × 305 ) / 1
LCM(231,305) = 70455 / 1
LCM(231,305) = 70455
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FAQs on GCF of Fractions of 176/231, 342/305
1. What is the HCF of 176,342?
The HCF of 176,342 is 2
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 176/231, 342/305?
Answer: GCF of Numerators as per given numbers 176/231, 342/305 is
GCF of Numerators i.e. for 176,342 is 2
LCM of denominators i.e. for 231,305 is 70455.
Thus, GCF of Fractions is 2/70455.Finally, GCF of Fractions for 176/231, 342/305 is 2/70455.