GCF of 580/65, 709/840
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 580/65, 709/840 i.e 1/10920 easily. The following is the detailed procedure to determine the greatest common factor of fractions 580/65, 709/840.
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 580/65,709/840?
Given fractions are 580/65,709/840
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 580/65,709/840, numerators are 580,709
Denominators are 65,840
The GCF of 580,709 is 1 .
LCM of 65,840 is 10920.
The greatest common factor of 580/65,709/840 = [GCF of 580,709]/[LCM of 65,840]= 1/10920
Therefore, the GCF of 580/65,709/840 is 1/10920.
To find the highest common factor of 580,709, we have to find the factors of both numbers and list the highest common factor.
The factors of 580 are 1, 2, 4, 5, 10, 20, 29, 58, 116, 145, 290, 580
The factors of 709 are 1, 709
The HCF of 580,709 is 1.
Lets's calculate GCF of 580,709
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 580,709 By Matching Biggest Common Factor Method
Now, list down the factors of 580
:1,2,4,5,10,20,29,58,116,145,290,580
Now, list down the factors of 709
:1,709
Greatest Common Factor
We found the factors 580,709 . The biggest common factor number is the GCF number.
So the greatest common factor 580,709 is 1.
Lets's calculate LCM of 65,840
| 5 | 65, 840 |
| 13, 168 |
∴ So the LCM of the given numbers is 5 x 13 x 168 = 10920
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/10920
Therefore, the GCF of Fractions 580/65,709/840 is 1/10920
Least Common Multiple of 65,840 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 65,840 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(65,840) = 5
common factors(in case of two or more numbers have common factors) = 1
GCF(65,840) x common factors =5 x 1 = 5
LCM(65,840) = ( 65 × 840 ) / 5
LCM(65,840) = 54600 / 5
LCM(65,840) = 10920
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FAQs on GCF of Fractions of 580/65, 709/840
1. What is the HCF of 580,709?
The HCF of 580,709 is 1
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 580/65, 709/840?
Answer: GCF of Numerators as per given numbers 580/65, 709/840 is
GCF of Numerators i.e. for 580,709 is 1
LCM of denominators i.e. for 65,840 is 10920.
Thus, GCF of Fractions is 1/10920.Finally, GCF of Fractions for 580/65, 709/840 is 1/10920.