GCF of 657/821, 774/498
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 657/821, 774/498 i.e 9/408858 easily. The following is the detailed procedure to determine the greatest common factor of fractions 657/821, 774/498.
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 657/821,774/498?
Given fractions are 657/821,774/498
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 657/821,774/498, numerators are 657,774
Denominators are 821,498
The GCF of 657,774 is 9 .
LCM of 821,498 is 408858.
The greatest common factor of 657/821,774/498 = [GCF of 657,774]/[LCM of 821,498]= 9/408858
Therefore, the GCF of 657/821,774/498 is 9/408858.
To find the highest common factor of 657,774, we have to find the factors of both numbers and list the highest common factor.
The factors of 657 are 1, 3, 9, 73, 219, 657
The factors of 774 are 1, 2, 3, 6, 9, 18, 43, 86, 129, 258, 387, 774
The HCF of 657,774 is 9.
Lets's calculate GCF of 657,774
| 3 | 657, 774 |
| 3 | 219, 258 |
| 73, 86 |
∴ So the GCF of the given numbers is 3 x 3 = 9
Greatest Common Factor of 657,774 By Matching Biggest Common Factor Method
Now, list down the factors of 657
:1,3,9,73,219,657
Now, list down the factors of 774
:1,2,3,6,9,18,43,86,129,258,387,774
Greatest Common Factor
We found the factors 657,774 . The biggest common factor number is the GCF number.
So the greatest common factor 657,774 is 9.
Lets's calculate LCM of 821,498
Given numbers has no common factors except 1. So, there LCM is their product i.e 408858
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 9/408858
Therefore, the GCF of Fractions 657/821,774/498 is 9/408858
Least Common Multiple of 821,498 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 821,498 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(821,498) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(821,498) x common factors =1 x 1 = 1
LCM(821,498) = ( 821 × 498 ) / 1
LCM(821,498) = 408858 / 1
LCM(821,498) = 408858
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FAQs on GCF of Fractions of 657/821, 774/498
1. What is the HCF of 657,774?
The HCF of 657,774 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 657/821, 774/498?
Answer: GCF of Numerators as per given numbers 657/821, 774/498 is
GCF of Numerators i.e. for 657,774 is 9
LCM of denominators i.e. for 821,498 is 408858.
Thus, GCF of Fractions is 9/408858.Finally, GCF of Fractions for 657/821, 774/498 is 9/408858.