GCF of 807/278, 729/614
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 807/278, 729/614 i.e 3/85346 easily. The following is the detailed procedure to determine the greatest common factor of fractions 807/278, 729/614.
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 807/278,729/614?
Given fractions are 807/278,729/614
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 807/278,729/614, numerators are 807,729
Denominators are 278,614
The GCF of 807,729 is 3 .
LCM of 278,614 is 85346.
The greatest common factor of 807/278,729/614 = [GCF of 807,729]/[LCM of 278,614]= 3/85346
Therefore, the GCF of 807/278,729/614 is 3/85346.
To find the highest common factor of 807,729, we have to find the factors of both numbers and list the highest common factor.
The factors of 807 are 1, 3, 269, 807
The factors of 729 are 1, 3, 9, 27, 81, 243, 729
The HCF of 807,729 is 3.
Lets's calculate GCF of 807,729
| 3 | 807, 729 |
| 269, 243 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 807,729 By Matching Biggest Common Factor Method
Now, list down the factors of 807
:1,3,269,807
Now, list down the factors of 729
:1,3,9,27,81,243,729
Greatest Common Factor
We found the factors 807,729 . The biggest common factor number is the GCF number.
So the greatest common factor 807,729 is 3.
Lets's calculate LCM of 278,614
| 2 | 278, 614 |
| 139, 307 |
∴ So the LCM of the given numbers is 2 x 139 x 307 = 85346
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/85346
Therefore, the GCF of Fractions 807/278,729/614 is 3/85346
Least Common Multiple of 278,614 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 278,614 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(278,614) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(278,614) x common factors =2 x 1 = 2
LCM(278,614) = ( 278 × 614 ) / 2
LCM(278,614) = 170692 / 2
LCM(278,614) = 85346
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FAQs on GCF of Fractions of 807/278, 729/614
1. What is the HCF of 807,729?
The HCF of 807,729 is 3
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 807/278, 729/614?
Answer: GCF of Numerators as per given numbers 807/278, 729/614 is
GCF of Numerators i.e. for 807,729 is 3
LCM of denominators i.e. for 278,614 is 85346.
Thus, GCF of Fractions is 3/85346.Finally, GCF of Fractions for 807/278, 729/614 is 3/85346.