GCF of 9724/548, 2178/8759
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 9724/548, 2178/8759 i.e 22/4799932 easily. The following is the detailed procedure to determine the greatest common factor of fractions 9724/548, 2178/8759.
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 9724/548,2178/8759?
Given fractions are 9724/548,2178/8759
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 9724/548,2178/8759, numerators are 9724,2178
Denominators are 548,8759
The GCF of 9724,2178 is 22 .
LCM of 548,8759 is 4799932.
The greatest common factor of 9724/548,2178/8759 = [GCF of 9724,2178]/[LCM of 548,8759]= 22/4799932
Therefore, the GCF of 9724/548,2178/8759 is 22/4799932.
To find the highest common factor of 9724,2178, we have to find the factors of both numbers and list the highest common factor.
The factors of 9724 are 1, 2, 4, 11, 13, 17, 22, 26, 34, 44, 52, 68, 143, 187, 221, 286, 374, 442, 572, 748, 884, 2431, 4862, 9724
The factors of 2178 are 1, 2, 3, 6, 9, 11, 18, 22, 33, 66, 99, 121, 198, 242, 363, 726, 1089, 2178
The HCF of 9724,2178 is 22.
Lets's calculate GCF of 9724,2178
| 2 | 9724, 2178 |
| 11 | 4862, 1089 |
| 442, 99 |
∴ So the GCF of the given numbers is 2 x 11 = 22
Greatest Common Factor of 9724,2178 By Matching Biggest Common Factor Method
Now, list down the factors of 9724
:1,2,4,11,13,17,22,26,34,44,52,68,143,187,221,286,374,442,572,748,884,2431,4862,9724
Now, list down the factors of 2178
:1,2,3,6,9,11,18,22,33,66,99,121,198,242,363,726,1089,2178
Greatest Common Factor
We found the factors 9724,2178 . The biggest common factor number is the GCF number.
So the greatest common factor 9724,2178 is 22.
Lets's calculate LCM of 548,8759
Given numbers has no common factors except 1. So, there LCM is their product i.e 4799932
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 22/4799932
Therefore, the GCF of Fractions 9724/548,2178/8759 is 22/4799932
Least Common Multiple of 548,8759 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 548,8759 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(548,8759) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(548,8759) x common factors =1 x 1 = 1
LCM(548,8759) = ( 548 × 8759 ) / 1
LCM(548,8759) = 4799932 / 1
LCM(548,8759) = 4799932
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FAQs on GCF of Fractions of 9724/548, 2178/8759
1. What is the HCF of 9724,2178?
The HCF of 9724,2178 is 22
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 9724/548, 2178/8759?
Answer: GCF of Numerators as per given numbers 9724/548, 2178/8759 is
GCF of Numerators i.e. for 9724,2178 is 22
LCM of denominators i.e. for 548,8759 is 4799932.
Thus, GCF of Fractions is 22/4799932.Finally, GCF of Fractions for 9724/548, 2178/8759 is 22/4799932.