GCF of 9714/986, 7756/2709
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 9714/986, 7756/2709 i.e 2/2671074 easily. The following is the detailed procedure to determine the greatest common factor of fractions 9714/986, 7756/2709.
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 9714/986,7756/2709?
Given fractions are 9714/986,7756/2709
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 9714/986,7756/2709, numerators are 9714,7756
Denominators are 986,2709
The GCF of 9714,7756 is 2 .
LCM of 986,2709 is 2671074.
The greatest common factor of 9714/986,7756/2709 = [GCF of 9714,7756]/[LCM of 986,2709]= 2/2671074
Therefore, the GCF of 9714/986,7756/2709 is 2/2671074.
To find the highest common factor of 9714,7756, we have to find the factors of both numbers and list the highest common factor.
The factors of 9714 are 1, 2, 3, 6, 1619, 3238, 4857, 9714
The factors of 7756 are 1, 2, 4, 7, 14, 28, 277, 554, 1108, 1939, 3878, 7756
The HCF of 9714,7756 is 2.
Lets's calculate GCF of 9714,7756
| 2 | 9714, 7756 |
| 4857, 3878 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 9714,7756 By Matching Biggest Common Factor Method
Now, list down the factors of 9714
:1,2,3,6,1619,3238,4857,9714
Now, list down the factors of 7756
:1,2,4,7,14,28,277,554,1108,1939,3878,7756
Greatest Common Factor
We found the factors 9714,7756 . The biggest common factor number is the GCF number.
So the greatest common factor 9714,7756 is 2.
Lets's calculate LCM of 986,2709
Given numbers has no common factors except 1. So, there LCM is their product i.e 2671074
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/2671074
Therefore, the GCF of Fractions 9714/986,7756/2709 is 2/2671074
Least Common Multiple of 986,2709 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 986,2709 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(986,2709) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(986,2709) x common factors =1 x 1 = 1
LCM(986,2709) = ( 986 × 2709 ) / 1
LCM(986,2709) = 2671074 / 1
LCM(986,2709) = 2671074
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FAQs on GCF of Fractions of 9714/986, 7756/2709
1. What is the HCF of 9714,7756?
The HCF of 9714,7756 is 2
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 9714/986, 7756/2709?
Answer: GCF of Numerators as per given numbers 9714/986, 7756/2709 is
GCF of Numerators i.e. for 9714,7756 is 2
LCM of denominators i.e. for 986,2709 is 2671074.
Thus, GCF of Fractions is 2/2671074.Finally, GCF of Fractions for 9714/986, 7756/2709 is 2/2671074.