GCF of 340/21, 138/627
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 340/21, 138/627 i.e 2/4389 easily. The following is the detailed procedure to determine the greatest common factor of fractions 340/21, 138/627.
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 340/21,138/627?
Given fractions are 340/21,138/627
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 340/21,138/627, numerators are 340,138
Denominators are 21,627
The GCF of 340,138 is 2 .
LCM of 21,627 is 4389.
The greatest common factor of 340/21,138/627 = [GCF of 340,138]/[LCM of 21,627]= 2/4389
Therefore, the GCF of 340/21,138/627 is 2/4389.
To find the highest common factor of 340,138, we have to find the factors of both numbers and list the highest common factor.
The factors of 340 are 1, 2, 4, 5, 10, 17, 20, 34, 68, 85, 170, 340
The factors of 138 are 1, 2, 3, 6, 23, 46, 69, 138
The HCF of 340,138 is 2.
Lets's calculate GCF of 340,138
| 2 | 340, 138 |
| 170, 69 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 340,138 By Matching Biggest Common Factor Method
Now, list down the factors of 340
:1,2,4,5,10,17,20,34,68,85,170,340
Now, list down the factors of 138
:1,2,3,6,23,46,69,138
Greatest Common Factor
We found the factors 340,138 . The biggest common factor number is the GCF number.
So the greatest common factor 340,138 is 2.
Lets's calculate LCM of 21,627
| 3 | 21, 627 |
| 7, 209 |
∴ So the LCM of the given numbers is 3 x 7 x 209 = 4389
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/4389
Therefore, the GCF of Fractions 340/21,138/627 is 2/4389
Least Common Multiple of 21,627 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 21,627 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(21,627) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(21,627) x common factors =3 x 1 = 3
LCM(21,627) = ( 21 × 627 ) / 3
LCM(21,627) = 13167 / 3
LCM(21,627) = 4389
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FAQs on GCF of Fractions of 340/21, 138/627
1. What is the HCF of 340,138?
The HCF of 340,138 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 340/21, 138/627?
Answer: GCF of Numerators as per given numbers 340/21, 138/627 is
GCF of Numerators i.e. for 340,138 is 2
LCM of denominators i.e. for 21,627 is 4389.
Thus, GCF of Fractions is 2/4389.Finally, GCF of Fractions for 340/21, 138/627 is 2/4389.