GCF of 9768/278, 7131/4688
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 9768/278, 7131/4688 i.e 3/651632 easily. The following is the detailed procedure to determine the greatest common factor of fractions 9768/278, 7131/4688.
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 9768/278,7131/4688?
Given fractions are 9768/278,7131/4688
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 9768/278,7131/4688, numerators are 9768,7131
Denominators are 278,4688
The GCF of 9768,7131 is 3 .
LCM of 278,4688 is 651632.
The greatest common factor of 9768/278,7131/4688 = [GCF of 9768,7131]/[LCM of 278,4688]= 3/651632
Therefore, the GCF of 9768/278,7131/4688 is 3/651632.
To find the highest common factor of 9768,7131, we have to find the factors of both numbers and list the highest common factor.
The factors of 9768 are 1, 2, 3, 4, 6, 8, 11, 12, 22, 24, 33, 37, 44, 66, 74, 88, 111, 132, 148, 222, 264, 296, 407, 444, 814, 888, 1221, 1628, 2442, 3256, 4884, 9768
The factors of 7131 are 1, 3, 2377, 7131
The HCF of 9768,7131 is 3.
Lets's calculate GCF of 9768,7131
| 3 | 9768, 7131 |
| 3256, 2377 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 9768,7131 By Matching Biggest Common Factor Method
Now, list down the factors of 9768
:1,2,3,4,6,8,11,12,22,24,33,37,44,66,74,88,111,132,148,222,264,296,407,444,814,888,1221,1628,2442,3256,4884,9768
Now, list down the factors of 7131
:1,3,2377,7131
Greatest Common Factor
We found the factors 9768,7131 . The biggest common factor number is the GCF number.
So the greatest common factor 9768,7131 is 3.
Lets's calculate LCM of 278,4688
| 2 | 278, 4688 |
| 139, 2344 |
∴ So the LCM of the given numbers is 2 x 139 x 2344 = 651632
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/651632
Therefore, the GCF of Fractions 9768/278,7131/4688 is 3/651632
Least Common Multiple of 278,4688 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 278,4688 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(278,4688) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(278,4688) x common factors =2 x 1 = 2
LCM(278,4688) = ( 278 × 4688 ) / 2
LCM(278,4688) = 1303264 / 2
LCM(278,4688) = 651632
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FAQs on GCF of Fractions of 9768/278, 7131/4688
1. What is the HCF of 9768,7131?
The HCF of 9768,7131 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 9768/278, 7131/4688?
Answer: GCF of Numerators as per given numbers 9768/278, 7131/4688 is
GCF of Numerators i.e. for 9768,7131 is 3
LCM of denominators i.e. for 278,4688 is 651632.
Thus, GCF of Fractions is 3/651632.Finally, GCF of Fractions for 9768/278, 7131/4688 is 3/651632.