GCF of 9724/344, 4459/7772
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 9724/344, 4459/7772 i.e 13/668392 easily. The following is the detailed procedure to determine the greatest common factor of fractions 9724/344, 4459/7772.
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 9724/344,4459/7772?
Given fractions are 9724/344,4459/7772
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 9724/344,4459/7772, numerators are 9724,4459
Denominators are 344,7772
The GCF of 9724,4459 is 13 .
LCM of 344,7772 is 668392.
The greatest common factor of 9724/344,4459/7772 = [GCF of 9724,4459]/[LCM of 344,7772]= 13/668392
Therefore, the GCF of 9724/344,4459/7772 is 13/668392.
To find the highest common factor of 9724,4459, we have to find the factors of both numbers and list the highest common factor.
The factors of 9724 are 1, 2, 4, 11, 13, 17, 22, 26, 34, 44, 52, 68, 143, 187, 221, 286, 374, 442, 572, 748, 884, 2431, 4862, 9724
The factors of 4459 are 1, 7, 13, 49, 91, 343, 637, 4459
The HCF of 9724,4459 is 13.
Lets's calculate GCF of 9724,4459
| 13 | 9724, 4459 |
| 748, 343 |
∴ So the GCF of the given numbers is 13 = 13
Greatest Common Factor of 9724,4459 By Matching Biggest Common Factor Method
Now, list down the factors of 9724
:1,2,4,11,13,17,22,26,34,44,52,68,143,187,221,286,374,442,572,748,884,2431,4862,9724
Now, list down the factors of 4459
:1,7,13,49,91,343,637,4459
Greatest Common Factor
We found the factors 9724,4459 . The biggest common factor number is the GCF number.
So the greatest common factor 9724,4459 is 13.
Lets's calculate LCM of 344,7772
| 2 | 344, 7772 |
| 2 | 172, 3886 |
| 86, 1943 |
∴ So the LCM of the given numbers is 2 x 2 x 86 x 1943 = 668392
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 13/668392
Therefore, the GCF of Fractions 9724/344,4459/7772 is 13/668392
Least Common Multiple of 344,7772 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 344,7772 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(344,7772) = 4
common factors(in case of two or more numbers have common factors) = 1
GCF(344,7772) x common factors =4 x 1 = 4
LCM(344,7772) = ( 344 × 7772 ) / 4
LCM(344,7772) = 2673568 / 4
LCM(344,7772) = 668392
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FAQs on GCF of Fractions of 9724/344, 4459/7772
1. What is the HCF of 9724,4459?
The HCF of 9724,4459 is 13
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 9724/344, 4459/7772?
Answer: GCF of Numerators as per given numbers 9724/344, 4459/7772 is
GCF of Numerators i.e. for 9724,4459 is 13
LCM of denominators i.e. for 344,7772 is 668392.
Thus, GCF of Fractions is 13/668392.Finally, GCF of Fractions for 9724/344, 4459/7772 is 13/668392.