GCF of 873/30, 678/141
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 873/30, 678/141 i.e 3/1410 easily. The following is the detailed procedure to determine the greatest common factor of fractions 873/30, 678/141.
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 873/30,678/141?
Given fractions are 873/30,678/141
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 873/30,678/141, numerators are 873,678
Denominators are 30,141
The GCF of 873,678 is 3 .
LCM of 30,141 is 1410.
The greatest common factor of 873/30,678/141 = [GCF of 873,678]/[LCM of 30,141]= 3/1410
Therefore, the GCF of 873/30,678/141 is 3/1410.
To find the highest common factor of 873,678, we have to find the factors of both numbers and list the highest common factor.
The factors of 873 are 1, 3, 9, 97, 291, 873
The factors of 678 are 1, 2, 3, 6, 113, 226, 339, 678
The HCF of 873,678 is 3.
Lets's calculate GCF of 873,678
| 3 | 873, 678 |
| 291, 226 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 873,678 By Matching Biggest Common Factor Method
Now, list down the factors of 873
:1,3,9,97,291,873
Now, list down the factors of 678
:1,2,3,6,113,226,339,678
Greatest Common Factor
We found the factors 873,678 . The biggest common factor number is the GCF number.
So the greatest common factor 873,678 is 3.
Lets's calculate LCM of 30,141
| 3 | 30, 141 |
| 10, 47 |
∴ So the LCM of the given numbers is 3 x 10 x 47 = 1410
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/1410
Therefore, the GCF of Fractions 873/30,678/141 is 3/1410
Least Common Multiple of 30,141 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 30,141 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(30,141) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(30,141) x common factors =3 x 1 = 3
LCM(30,141) = ( 30 × 141 ) / 3
LCM(30,141) = 4230 / 3
LCM(30,141) = 1410
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FAQs on GCF of Fractions of 873/30, 678/141
1. What is the HCF of 873,678?
The HCF of 873,678 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 873/30, 678/141?
Answer: GCF of Numerators as per given numbers 873/30, 678/141 is
GCF of Numerators i.e. for 873,678 is 3
LCM of denominators i.e. for 30,141 is 1410.
Thus, GCF of Fractions is 3/1410.Finally, GCF of Fractions for 873/30, 678/141 is 3/1410.