GCF of 340/65, 870/697
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 340/65, 870/697 i.e 10/45305 easily. The following is the detailed procedure to determine the greatest common factor of fractions 340/65, 870/697.
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 340/65,870/697?
Given fractions are 340/65,870/697
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 340/65,870/697, numerators are 340,870
Denominators are 65,697
The GCF of 340,870 is 10 .
LCM of 65,697 is 45305.
The greatest common factor of 340/65,870/697 = [GCF of 340,870]/[LCM of 65,697]= 10/45305
Therefore, the GCF of 340/65,870/697 is 10/45305.
To find the highest common factor of 340,870, 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 870 are 1, 2, 3, 5, 6, 10, 15, 29, 30, 58, 87, 145, 174, 290, 435, 870
The HCF of 340,870 is 10.
Lets's calculate GCF of 340,870
| 2 | 340, 870 |
| 5 | 170, 435 |
| 34, 87 |
∴ So the GCF of the given numbers is 2 x 5 = 10
Greatest Common Factor of 340,870 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 870
:1,2,3,5,6,10,15,29,30,58,87,145,174,290,435,870
Greatest Common Factor
We found the factors 340,870 . The biggest common factor number is the GCF number.
So the greatest common factor 340,870 is 10.
Lets's calculate LCM of 65,697
Given numbers has no common factors except 1. So, there LCM is their product i.e 45305
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 10/45305
Therefore, the GCF of Fractions 340/65,870/697 is 10/45305
Least Common Multiple of 65,697 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 65,697 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(65,697) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(65,697) x common factors =1 x 1 = 1
LCM(65,697) = ( 65 × 697 ) / 1
LCM(65,697) = 45305 / 1
LCM(65,697) = 45305
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FAQs on GCF of Fractions of 340/65, 870/697
1. What is the HCF of 340,870?
The HCF of 340,870 is 10
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 340/65, 870/697?
Answer: GCF of Numerators as per given numbers 340/65, 870/697 is
GCF of Numerators i.e. for 340,870 is 10
LCM of denominators i.e. for 65,697 is 45305.
Thus, GCF of Fractions is 10/45305.Finally, GCF of Fractions for 340/65, 870/697 is 10/45305.