GCF of 819/689, 1413/722
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 819/689, 1413/722 i.e 9/497458 easily. The following is the detailed procedure to determine the greatest common factor of fractions 819/689, 1413/722.
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 819/689,1413/722?
Given fractions are 819/689,1413/722
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 819/689,1413/722, numerators are 819,1413
Denominators are 689,722
The GCF of 819,1413 is 9 .
LCM of 689,722 is 497458.
The greatest common factor of 819/689,1413/722 = [GCF of 819,1413]/[LCM of 689,722]= 9/497458
Therefore, the GCF of 819/689,1413/722 is 9/497458.
To find the highest common factor of 819,1413, we have to find the factors of both numbers and list the highest common factor.
The factors of 819 are 1, 3, 7, 9, 13, 21, 39, 63, 91, 117, 273, 819
The factors of 1413 are 1, 3, 9, 157, 471, 1413
The HCF of 819,1413 is 9.
Lets's calculate GCF of 819,1413
| 3 | 819, 1413 |
| 3 | 273, 471 |
| 91, 157 |
∴ So the GCF of the given numbers is 3 x 3 = 9
Greatest Common Factor of 819,1413 By Matching Biggest Common Factor Method
Now, list down the factors of 819
:1,3,7,9,13,21,39,63,91,117,273,819
Now, list down the factors of 1413
:1,3,9,157,471,1413
Greatest Common Factor
We found the factors 819,1413 . The biggest common factor number is the GCF number.
So the greatest common factor 819,1413 is 9.
Lets's calculate LCM of 689,722
Given numbers has no common factors except 1. So, there LCM is their product i.e 497458
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 9/497458
Therefore, the GCF of Fractions 819/689,1413/722 is 9/497458
Least Common Multiple of 689,722 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 689,722 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(689,722) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(689,722) x common factors =1 x 1 = 1
LCM(689,722) = ( 689 × 722 ) / 1
LCM(689,722) = 497458 / 1
LCM(689,722) = 497458
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FAQs on GCF of Fractions of 819/689, 1413/722
1. What is the HCF of 819,1413?
The HCF of 819,1413 is 9
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 819/689, 1413/722?
Answer: GCF of Numerators as per given numbers 819/689, 1413/722 is
GCF of Numerators i.e. for 819,1413 is 9
LCM of denominators i.e. for 689,722 is 497458.
Thus, GCF of Fractions is 9/497458.Finally, GCF of Fractions for 819/689, 1413/722 is 9/497458.