GCF of 276/686, 9765/3104
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 276/686, 9765/3104 i.e 3/1064672 easily. The following is the detailed procedure to determine the greatest common factor of fractions 276/686, 9765/3104.
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 276/686,9765/3104?
Given fractions are 276/686,9765/3104
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 276/686,9765/3104, numerators are 276,9765
Denominators are 686,3104
The GCF of 276,9765 is 3 .
LCM of 686,3104 is 1064672.
The greatest common factor of 276/686,9765/3104 = [GCF of 276,9765]/[LCM of 686,3104]= 3/1064672
Therefore, the GCF of 276/686,9765/3104 is 3/1064672.
To find the highest common factor of 276,9765, we have to find the factors of both numbers and list the highest common factor.
The factors of 276 are 1, 2, 3, 4, 6, 12, 23, 46, 69, 92, 138, 276
The factors of 9765 are 1, 3, 5, 7, 9, 15, 21, 31, 35, 45, 63, 93, 105, 155, 217, 279, 315, 465, 651, 1085, 1395, 1953, 3255, 9765
The HCF of 276,9765 is 3.
Lets's calculate GCF of 276,9765
| 3 | 276, 9765 |
| 92, 3255 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 276,9765 By Matching Biggest Common Factor Method
Now, list down the factors of 276
:1,2,3,4,6,12,23,46,69,92,138,276
Now, list down the factors of 9765
:1,3,5,7,9,15,21,31,35,45,63,93,105,155,217,279,315,465,651,1085,1395,1953,3255,9765
Greatest Common Factor
We found the factors 276,9765 . The biggest common factor number is the GCF number.
So the greatest common factor 276,9765 is 3.
Lets's calculate LCM of 686,3104
| 2 | 686, 3104 |
| 343, 1552 |
∴ So the LCM of the given numbers is 2 x 343 x 1552 = 1064672
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/1064672
Therefore, the GCF of Fractions 276/686,9765/3104 is 3/1064672
Least Common Multiple of 686,3104 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 686,3104 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(686,3104) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(686,3104) x common factors =2 x 1 = 2
LCM(686,3104) = ( 686 × 3104 ) / 2
LCM(686,3104) = 2129344 / 2
LCM(686,3104) = 1064672
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FAQs on GCF of Fractions of 276/686, 9765/3104
1. What is the HCF of 276,9765?
The HCF of 276,9765 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 276/686, 9765/3104?
Answer: GCF of Numerators as per given numbers 276/686, 9765/3104 is
GCF of Numerators i.e. for 276,9765 is 3
LCM of denominators i.e. for 686,3104 is 1064672.
Thus, GCF of Fractions is 3/1064672.Finally, GCF of Fractions for 276/686, 9765/3104 is 3/1064672.