GCF of 872/309, 654/627
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 872/309, 654/627 i.e 218/64581 easily. The following is the detailed procedure to determine the greatest common factor of fractions 872/309, 654/627.
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 872/309,654/627?
Given fractions are 872/309,654/627
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 872/309,654/627, numerators are 872,654
Denominators are 309,627
The GCF of 872,654 is 218 .
LCM of 309,627 is 64581.
The greatest common factor of 872/309,654/627 = [GCF of 872,654]/[LCM of 309,627]= 218/64581
Therefore, the GCF of 872/309,654/627 is 218/64581.
To find the highest common factor of 872,654, we have to find the factors of both numbers and list the highest common factor.
The factors of 872 are 1, 2, 4, 8, 109, 218, 436, 872
The factors of 654 are 1, 2, 3, 6, 109, 218, 327, 654
The HCF of 872,654 is 218.
Lets's calculate GCF of 872,654
| 2 | 872, 654 |
| 109 | 436, 327 |
| 4, 3 |
∴ So the GCF of the given numbers is 2 x 109 = 218
Greatest Common Factor of 872,654 By Matching Biggest Common Factor Method
Now, list down the factors of 872
:1,2,4,8,109,218,436,872
Now, list down the factors of 654
:1,2,3,6,109,218,327,654
Greatest Common Factor
We found the factors 872,654 . The biggest common factor number is the GCF number.
So the greatest common factor 872,654 is 218.
Lets's calculate LCM of 309,627
| 3 | 309, 627 |
| 103, 209 |
∴ So the LCM of the given numbers is 3 x 103 x 209 = 64581
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 218/64581
Therefore, the GCF of Fractions 872/309,654/627 is 218/64581
Least Common Multiple of 309,627 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 309,627 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(309,627) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(309,627) x common factors =3 x 1 = 3
LCM(309,627) = ( 309 × 627 ) / 3
LCM(309,627) = 193743 / 3
LCM(309,627) = 64581
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FAQs on GCF of Fractions of 872/309, 654/627
1. What is the HCF of 872,654?
The HCF of 872,654 is 218
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 872/309, 654/627?
Answer: GCF of Numerators as per given numbers 872/309, 654/627 is
GCF of Numerators i.e. for 872,654 is 218
LCM of denominators i.e. for 309,627 is 64581.
Thus, GCF of Fractions is 218/64581.Finally, GCF of Fractions for 872/309, 654/627 is 218/64581.