GCF of 580/684, 1969/770
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 580/684, 1969/770 i.e 1/263340 easily. The following is the detailed procedure to determine the greatest common factor of fractions 580/684, 1969/770.
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 580/684,1969/770?
Given fractions are 580/684,1969/770
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 580/684,1969/770, numerators are 580,1969
Denominators are 684,770
The GCF of 580,1969 is 1 .
LCM of 684,770 is 263340.
The greatest common factor of 580/684,1969/770 = [GCF of 580,1969]/[LCM of 684,770]= 1/263340
Therefore, the GCF of 580/684,1969/770 is 1/263340.
To find the highest common factor of 580,1969, 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 1969 are 1, 11, 179, 1969
The HCF of 580,1969 is 1.
Lets's calculate GCF of 580,1969
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 580,1969 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 1969
:1,11,179,1969
Greatest Common Factor
We found the factors 580,1969 . The biggest common factor number is the GCF number.
So the greatest common factor 580,1969 is 1.
Lets's calculate LCM of 684,770
| 2 | 684, 770 |
| 342, 385 |
∴ So the LCM of the given numbers is 2 x 342 x 385 = 263340
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/263340
Therefore, the GCF of Fractions 580/684,1969/770 is 1/263340
Least Common Multiple of 684,770 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 684,770 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(684,770) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(684,770) x common factors =2 x 1 = 2
LCM(684,770) = ( 684 × 770 ) / 2
LCM(684,770) = 526680 / 2
LCM(684,770) = 263340
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FAQs on GCF of Fractions of 580/684, 1969/770
1. What is the HCF of 580,1969?
The HCF of 580,1969 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 580/684, 1969/770?
Answer: GCF of Numerators as per given numbers 580/684, 1969/770 is
GCF of Numerators i.e. for 580,1969 is 1
LCM of denominators i.e. for 684,770 is 263340.
Thus, GCF of Fractions is 1/263340.Finally, GCF of Fractions for 580/684, 1969/770 is 1/263340.