GCF of 114/10, 684/842
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 114/10, 684/842 i.e 114/4210 easily. The following is the detailed procedure to determine the greatest common factor of fractions 114/10, 684/842.
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 114/10,684/842?
Given fractions are 114/10,684/842
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 114/10,684/842, numerators are 114,684
Denominators are 10,842
The GCF of 114,684 is 114 .
LCM of 10,842 is 4210.
The greatest common factor of 114/10,684/842 = [GCF of 114,684]/[LCM of 10,842]= 114/4210
Therefore, the GCF of 114/10,684/842 is 114/4210.
To find the highest common factor of 114,684, 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 684 are 1, 2, 3, 4, 6, 9, 12, 18, 19, 36, 38, 57, 76, 114, 171, 228, 342, 684
The HCF of 114,684 is 114.
Lets's calculate GCF of 114,684
| 2 | 114, 684 |
| 3 | 57, 342 |
| 19 | 19, 114 |
| 1, 6 |
∴ So the GCF of the given numbers is 2 x 3 x 19 = 114
Greatest Common Factor of 114,684 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 684
:1,2,3,4,6,9,12,18,19,36,38,57,76,114,171,228,342,684
Greatest Common Factor
We found the factors 114,684 . The biggest common factor number is the GCF number.
So the greatest common factor 114,684 is 114.
Lets's calculate LCM of 10,842
| 2 | 10, 842 |
| 5, 421 |
∴ So the LCM of the given numbers is 2 x 5 x 421 = 4210
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 114/4210
Therefore, the GCF of Fractions 114/10,684/842 is 114/4210
Least Common Multiple of 10,842 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 10,842 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(10,842) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(10,842) x common factors =2 x 1 = 2
LCM(10,842) = ( 10 × 842 ) / 2
LCM(10,842) = 8420 / 2
LCM(10,842) = 4210
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FAQs on GCF of Fractions of 114/10, 684/842
1. What is the HCF of 114,684?
The HCF of 114,684 is 114
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 114/10, 684/842?
Answer: GCF of Numerators as per given numbers 114/10, 684/842 is
GCF of Numerators i.e. for 114,684 is 114
LCM of denominators i.e. for 10,842 is 4210.
Thus, GCF of Fractions is 114/4210.Finally, GCF of Fractions for 114/10, 684/842 is 114/4210.