GCF of 7698/764, 3459/7704
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 7698/764, 3459/7704 i.e 3/1471464 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7698/764, 3459/7704.
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 7698/764,3459/7704?
Given fractions are 7698/764,3459/7704
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 7698/764,3459/7704, numerators are 7698,3459
Denominators are 764,7704
The GCF of 7698,3459 is 3 .
LCM of 764,7704 is 1471464.
The greatest common factor of 7698/764,3459/7704 = [GCF of 7698,3459]/[LCM of 764,7704]= 3/1471464
Therefore, the GCF of 7698/764,3459/7704 is 3/1471464.
To find the highest common factor of 7698,3459, we have to find the factors of both numbers and list the highest common factor.
The factors of 7698 are 1, 2, 3, 6, 1283, 2566, 3849, 7698
The factors of 3459 are 1, 3, 1153, 3459
The HCF of 7698,3459 is 3.
Lets's calculate GCF of 7698,3459
| 3 | 7698, 3459 |
| 2566, 1153 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 7698,3459 By Matching Biggest Common Factor Method
Now, list down the factors of 7698
:1,2,3,6,1283,2566,3849,7698
Now, list down the factors of 3459
:1,3,1153,3459
Greatest Common Factor
We found the factors 7698,3459 . The biggest common factor number is the GCF number.
So the greatest common factor 7698,3459 is 3.
Lets's calculate LCM of 764,7704
| 2 | 764, 7704 |
| 2 | 382, 3852 |
| 191, 1926 |
∴ So the LCM of the given numbers is 2 x 2 x 191 x 1926 = 1471464
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/1471464
Therefore, the GCF of Fractions 7698/764,3459/7704 is 3/1471464
Least Common Multiple of 764,7704 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 764,7704 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(764,7704) = 4
common factors(in case of two or more numbers have common factors) = 1
GCF(764,7704) x common factors =4 x 1 = 4
LCM(764,7704) = ( 764 × 7704 ) / 4
LCM(764,7704) = 5885856 / 4
LCM(764,7704) = 1471464
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FAQs on GCF of Fractions of 7698/764, 3459/7704
1. What is the HCF of 7698,3459?
The HCF of 7698,3459 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 7698/764, 3459/7704?
Answer: GCF of Numerators as per given numbers 7698/764, 3459/7704 is
GCF of Numerators i.e. for 7698,3459 is 3
LCM of denominators i.e. for 764,7704 is 1471464.
Thus, GCF of Fractions is 3/1471464.Finally, GCF of Fractions for 7698/764, 3459/7704 is 3/1471464.