GCF of 7734/585, 7707/5176
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 7734/585, 7707/5176 i.e 3/3027960 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7734/585, 7707/5176.
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 7734/585,7707/5176?
Given fractions are 7734/585,7707/5176
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 7734/585,7707/5176, numerators are 7734,7707
Denominators are 585,5176
The GCF of 7734,7707 is 3 .
LCM of 585,5176 is 3027960.
The greatest common factor of 7734/585,7707/5176 = [GCF of 7734,7707]/[LCM of 585,5176]= 3/3027960
Therefore, the GCF of 7734/585,7707/5176 is 3/3027960.
To find the highest common factor of 7734,7707, we have to find the factors of both numbers and list the highest common factor.
The factors of 7734 are 1, 2, 3, 6, 1289, 2578, 3867, 7734
The factors of 7707 are 1, 3, 7, 21, 367, 1101, 2569, 7707
The HCF of 7734,7707 is 3.
Lets's calculate GCF of 7734,7707
| 3 | 7734, 7707 |
| 2578, 2569 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 7734,7707 By Matching Biggest Common Factor Method
Now, list down the factors of 7734
:1,2,3,6,1289,2578,3867,7734
Now, list down the factors of 7707
:1,3,7,21,367,1101,2569,7707
Greatest Common Factor
We found the factors 7734,7707 . The biggest common factor number is the GCF number.
So the greatest common factor 7734,7707 is 3.
Lets's calculate LCM of 585,5176
Given numbers has no common factors except 1. So, there LCM is their product i.e 3027960
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/3027960
Therefore, the GCF of Fractions 7734/585,7707/5176 is 3/3027960
Least Common Multiple of 585,5176 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 585,5176 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(585,5176) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(585,5176) x common factors =1 x 1 = 1
LCM(585,5176) = ( 585 × 5176 ) / 1
LCM(585,5176) = 3027960 / 1
LCM(585,5176) = 3027960
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FAQs on GCF of Fractions of 7734/585, 7707/5176
1. What is the HCF of 7734,7707?
The HCF of 7734,7707 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 7734/585, 7707/5176?
Answer: GCF of Numerators as per given numbers 7734/585, 7707/5176 is
GCF of Numerators i.e. for 7734,7707 is 3
LCM of denominators i.e. for 585,5176 is 3027960.
Thus, GCF of Fractions is 3/3027960.Finally, GCF of Fractions for 7734/585, 7707/5176 is 3/3027960.