GCF of 7744/840, 9758/5032
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 7744/840, 9758/5032 i.e 2/528360 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7744/840, 9758/5032.
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 7744/840,9758/5032?
Given fractions are 7744/840,9758/5032
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 7744/840,9758/5032, numerators are 7744,9758
Denominators are 840,5032
The GCF of 7744,9758 is 2 .
LCM of 840,5032 is 528360.
The greatest common factor of 7744/840,9758/5032 = [GCF of 7744,9758]/[LCM of 840,5032]= 2/528360
Therefore, the GCF of 7744/840,9758/5032 is 2/528360.
To find the highest common factor of 7744,9758, we have to find the factors of both numbers and list the highest common factor.
The factors of 7744 are 1, 2, 4, 8, 11, 16, 22, 32, 44, 64, 88, 121, 176, 242, 352, 484, 704, 968, 1936, 3872, 7744
The factors of 9758 are 1, 2, 7, 14, 17, 34, 41, 82, 119, 238, 287, 574, 697, 1394, 4879, 9758
The HCF of 7744,9758 is 2.
Lets's calculate GCF of 7744,9758
| 2 | 7744, 9758 |
| 3872, 4879 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 7744,9758 By Matching Biggest Common Factor Method
Now, list down the factors of 7744
:1,2,4,8,11,16,22,32,44,64,88,121,176,242,352,484,704,968,1936,3872,7744
Now, list down the factors of 9758
:1,2,7,14,17,34,41,82,119,238,287,574,697,1394,4879,9758
Greatest Common Factor
We found the factors 7744,9758 . The biggest common factor number is the GCF number.
So the greatest common factor 7744,9758 is 2.
Lets's calculate LCM of 840,5032
| 2 | 840, 5032 |
| 2 | 420, 2516 |
| 2 | 210, 1258 |
| 105, 629 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 105 x 629 = 528360
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/528360
Therefore, the GCF of Fractions 7744/840,9758/5032 is 2/528360
Least Common Multiple of 840,5032 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 840,5032 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(840,5032) = 8
common factors(in case of two or more numbers have common factors) = 1
GCF(840,5032) x common factors =8 x 1 = 8
LCM(840,5032) = ( 840 × 5032 ) / 8
LCM(840,5032) = 4226880 / 8
LCM(840,5032) = 528360
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FAQs on GCF of Fractions of 7744/840, 9758/5032
1. What is the HCF of 7744,9758?
The HCF of 7744,9758 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 7744/840, 9758/5032?
Answer: GCF of Numerators as per given numbers 7744/840, 9758/5032 is
GCF of Numerators i.e. for 7744,9758 is 2
LCM of denominators i.e. for 840,5032 is 528360.
Thus, GCF of Fractions is 2/528360.Finally, GCF of Fractions for 7744/840, 9758/5032 is 2/528360.