GCF of 7692/834, 1785/4112
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 7692/834, 1785/4112 i.e 3/1714704 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7692/834, 1785/4112.
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 7692/834,1785/4112?
Given fractions are 7692/834,1785/4112
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 7692/834,1785/4112, numerators are 7692,1785
Denominators are 834,4112
The GCF of 7692,1785 is 3 .
LCM of 834,4112 is 1714704.
The greatest common factor of 7692/834,1785/4112 = [GCF of 7692,1785]/[LCM of 834,4112]= 3/1714704
Therefore, the GCF of 7692/834,1785/4112 is 3/1714704.
To find the highest common factor of 7692,1785, we have to find the factors of both numbers and list the highest common factor.
The factors of 7692 are 1, 2, 3, 4, 6, 12, 641, 1282, 1923, 2564, 3846, 7692
The factors of 1785 are 1, 3, 5, 7, 15, 17, 21, 35, 51, 85, 105, 119, 255, 357, 595, 1785
The HCF of 7692,1785 is 3.
Lets's calculate GCF of 7692,1785
| 3 | 7692, 1785 |
| 2564, 595 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 7692,1785 By Matching Biggest Common Factor Method
Now, list down the factors of 7692
:1,2,3,4,6,12,641,1282,1923,2564,3846,7692
Now, list down the factors of 1785
:1,3,5,7,15,17,21,35,51,85,105,119,255,357,595,1785
Greatest Common Factor
We found the factors 7692,1785 . The biggest common factor number is the GCF number.
So the greatest common factor 7692,1785 is 3.
Lets's calculate LCM of 834,4112
| 2 | 834, 4112 |
| 417, 2056 |
∴ So the LCM of the given numbers is 2 x 417 x 2056 = 1714704
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/1714704
Therefore, the GCF of Fractions 7692/834,1785/4112 is 3/1714704
Least Common Multiple of 834,4112 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 834,4112 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(834,4112) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(834,4112) x common factors =2 x 1 = 2
LCM(834,4112) = ( 834 × 4112 ) / 2
LCM(834,4112) = 3429408 / 2
LCM(834,4112) = 1714704
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FAQs on GCF of Fractions of 7692/834, 1785/4112
1. What is the HCF of 7692,1785?
The HCF of 7692,1785 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 7692/834, 1785/4112?
Answer: GCF of Numerators as per given numbers 7692/834, 1785/4112 is
GCF of Numerators i.e. for 7692,1785 is 3
LCM of denominators i.e. for 834,4112 is 1714704.
Thus, GCF of Fractions is 3/1714704.Finally, GCF of Fractions for 7692/834, 1785/4112 is 3/1714704.