GCF of 774/268, 470/289
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 774/268, 470/289 i.e 2/77452 easily. The following is the detailed procedure to determine the greatest common factor of fractions 774/268, 470/289.
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 774/268,470/289?
Given fractions are 774/268,470/289
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 774/268,470/289, numerators are 774,470
Denominators are 268,289
The GCF of 774,470 is 2 .
LCM of 268,289 is 77452.
The greatest common factor of 774/268,470/289 = [GCF of 774,470]/[LCM of 268,289]= 2/77452
Therefore, the GCF of 774/268,470/289 is 2/77452.
To find the highest common factor of 774,470, we have to find the factors of both numbers and list the highest common factor.
The factors of 774 are 1, 2, 3, 6, 9, 18, 43, 86, 129, 258, 387, 774
The factors of 470 are 1, 2, 5, 10, 47, 94, 235, 470
The HCF of 774,470 is 2.
Lets's calculate GCF of 774,470
| 2 | 774, 470 |
| 387, 235 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 774,470 By Matching Biggest Common Factor Method
Now, list down the factors of 774
:1,2,3,6,9,18,43,86,129,258,387,774
Now, list down the factors of 470
:1,2,5,10,47,94,235,470
Greatest Common Factor
We found the factors 774,470 . The biggest common factor number is the GCF number.
So the greatest common factor 774,470 is 2.
Lets's calculate LCM of 268,289
Given numbers has no common factors except 1. So, there LCM is their product i.e 77452
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/77452
Therefore, the GCF of Fractions 774/268,470/289 is 2/77452
Least Common Multiple of 268,289 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 268,289 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(268,289) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(268,289) x common factors =1 x 1 = 1
LCM(268,289) = ( 268 × 289 ) / 1
LCM(268,289) = 77452 / 1
LCM(268,289) = 77452
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FAQs on GCF of Fractions of 774/268, 470/289
1. What is the HCF of 774,470?
The HCF of 774,470 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 774/268, 470/289?
Answer: GCF of Numerators as per given numbers 774/268, 470/289 is
GCF of Numerators i.e. for 774,470 is 2
LCM of denominators i.e. for 268,289 is 77452.
Thus, GCF of Fractions is 2/77452.Finally, GCF of Fractions for 774/268, 470/289 is 2/77452.