GCF of 114/174, 4312/1689
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 114/174, 4312/1689 i.e 2/97962 easily. The following is the detailed procedure to determine the greatest common factor of fractions 114/174, 4312/1689.
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 114/174,4312/1689?
Given fractions are 114/174,4312/1689
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 114/174,4312/1689, numerators are 114,4312
Denominators are 174,1689
The GCF of 114,4312 is 2 .
LCM of 174,1689 is 97962.
The greatest common factor of 114/174,4312/1689 = [GCF of 114,4312]/[LCM of 174,1689]= 2/97962
Therefore, the GCF of 114/174,4312/1689 is 2/97962.
To find the highest common factor of 114,4312, we have to find the factors of both numbers and list the highest common factor.
The factors of 114 are 1, 2, 3, 6, 19, 38, 57, 114
The factors of 4312 are 1, 2, 4, 7, 8, 11, 14, 22, 28, 44, 49, 56, 77, 88, 98, 154, 196, 308, 392, 539, 616, 1078, 2156, 4312
The HCF of 114,4312 is 2.
Lets's calculate GCF of 114,4312
| 2 | 114, 4312 |
| 57, 2156 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 114,4312 By Matching Biggest Common Factor Method
Now, list down the factors of 114
:1,2,3,6,19,38,57,114
Now, list down the factors of 4312
:1,2,4,7,8,11,14,22,28,44,49,56,77,88,98,154,196,308,392,539,616,1078,2156,4312
Greatest Common Factor
We found the factors 114,4312 . The biggest common factor number is the GCF number.
So the greatest common factor 114,4312 is 2.
Lets's calculate LCM of 174,1689
| 3 | 174, 1689 |
| 58, 563 |
∴ So the LCM of the given numbers is 3 x 58 x 563 = 97962
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/97962
Therefore, the GCF of Fractions 114/174,4312/1689 is 2/97962
Least Common Multiple of 174,1689 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 174,1689 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(174,1689) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(174,1689) x common factors =3 x 1 = 3
LCM(174,1689) = ( 174 × 1689 ) / 3
LCM(174,1689) = 293886 / 3
LCM(174,1689) = 97962
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FAQs on GCF of Fractions of 114/174, 4312/1689
1. What is the HCF of 114,4312?
The HCF of 114,4312 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 114/174, 4312/1689?
Answer: GCF of Numerators as per given numbers 114/174, 4312/1689 is
GCF of Numerators i.e. for 114,4312 is 2
LCM of denominators i.e. for 174,1689 is 97962.
Thus, GCF of Fractions is 2/97962.Finally, GCF of Fractions for 114/174, 4312/1689 is 2/97962.