GCF of 209/724, 978/744, 292/878
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 209/724, 978/744, 292/878 i.e 1/59117496 easily. The following is the detailed procedure to determine the greatest common factor of fractions 209/724, 978/744, 292/878.
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 209/724,978/744,292/878?
Given fractions are 209/724,978/744,292/878
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 209/724,978/744,292/878, numerators are 209,978,292
Denominators are 724,744,878
The GCF of 209,978,292 is 1 .
LCM of 724,744,878 is 59117496.
The greatest common factor of 209/724,978/744,292/878 = [GCF of 209,978,292]/[LCM of 724,744,878]= 1/59117496
Therefore, the GCF of 209/724,978/744,292/878 is 1/59117496.
To find the highest common factor of 209,978,292, we have to find the factors of both numbers and list the highest common factor.
The factors of 209 are 1, 11, 19, 209
The factors of 978 are 1, 2, 3, 6, 163, 326, 489, 978
The factors of 292 are 1, 2, 4, 73, 146, 292
The HCF of 209,978,292 is 1.
Lets's calculate GCF of 209,978,292
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 209,978,292 By Matching Biggest Common Factor Method
Now, list down the factors of 209
:1,11,19,209
Now, list down the factors of 978
:1,2,3,6,163,326,489,978
Now, list down the factors of 292
:1,2,4,73,146,292
Greatest Common Factor
We found the factors 209,978,292 . The biggest common factor number is the GCF number.
So the greatest common factor 209,978,292 is 1.
Lets's calculate LCM of 724,744,878
| 2 | 724, 744, 878 |
| 2 | 362, 372, 439 |
| 181, 186, 439 |
∴ So the LCM of the given numbers is 2 x 2 x 181 x 186 x 439 = 59117496
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/59117496
Therefore, the GCF of Fractions 209/724,978/744,292/878 is 1/59117496
Least Common Multiple of 724,744,878 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 724,744,878 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(724,744,878) = 2
common factors(in case of two or more numbers have common factors) = 4
GCF(724,744,878) x common factors =2 x 4 = 8
LCM(724,744,878) = ( 724 × 744 × 878 ) / 8
LCM(724,744,878) = 472939968 / 8
LCM(724,744,878) = 59117496
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FAQs on GCF of Fractions of 209/724, 978/744, 292/878
1. What is the HCF of 209,978,292?
The HCF of 209,978,292 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 209/724, 978/744, 292/878?
Answer: GCF of Numerators as per given numbers 209/724, 978/744, 292/878 is
GCF of Numerators i.e. for 209,978,292 is 1
LCM of denominators i.e. for 724,744,878 is 59117496.
Thus, GCF of Fractions is 1/59117496.Finally, GCF of Fractions for 209/724, 978/744, 292/878 is 1/59117496.