GCF of 7758/408, 9618/9752
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 7758/408, 9618/9752 i.e 6/497352 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7758/408, 9618/9752.
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 7758/408,9618/9752?
Given fractions are 7758/408,9618/9752
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 7758/408,9618/9752, numerators are 7758,9618
Denominators are 408,9752
The GCF of 7758,9618 is 6 .
LCM of 408,9752 is 497352.
The greatest common factor of 7758/408,9618/9752 = [GCF of 7758,9618]/[LCM of 408,9752]= 6/497352
Therefore, the GCF of 7758/408,9618/9752 is 6/497352.
To find the highest common factor of 7758,9618, we have to find the factors of both numbers and list the highest common factor.
The factors of 7758 are 1, 2, 3, 6, 9, 18, 431, 862, 1293, 2586, 3879, 7758
The factors of 9618 are 1, 2, 3, 6, 7, 14, 21, 42, 229, 458, 687, 1374, 1603, 3206, 4809, 9618
The HCF of 7758,9618 is 6.
Lets's calculate GCF of 7758,9618
| 2 | 7758, 9618 |
| 3 | 3879, 4809 |
| 1293, 1603 |
∴ So the GCF of the given numbers is 2 x 3 = 6
Greatest Common Factor of 7758,9618 By Matching Biggest Common Factor Method
Now, list down the factors of 7758
:1,2,3,6,9,18,431,862,1293,2586,3879,7758
Now, list down the factors of 9618
:1,2,3,6,7,14,21,42,229,458,687,1374,1603,3206,4809,9618
Greatest Common Factor
We found the factors 7758,9618 . The biggest common factor number is the GCF number.
So the greatest common factor 7758,9618 is 6.
Lets's calculate LCM of 408,9752
| 2 | 408, 9752 |
| 2 | 204, 4876 |
| 2 | 102, 2438 |
| 51, 1219 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 51 x 1219 = 497352
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/497352
Therefore, the GCF of Fractions 7758/408,9618/9752 is 6/497352
Least Common Multiple of 408,9752 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 408,9752 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(408,9752) = 8
common factors(in case of two or more numbers have common factors) = 1
GCF(408,9752) x common factors =8 x 1 = 8
LCM(408,9752) = ( 408 × 9752 ) / 8
LCM(408,9752) = 3978816 / 8
LCM(408,9752) = 497352
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FAQs on GCF of Fractions of 7758/408, 9618/9752
1. What is the HCF of 7758,9618?
The HCF of 7758,9618 is 6
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 7758/408, 9618/9752?
Answer: GCF of Numerators as per given numbers 7758/408, 9618/9752 is
GCF of Numerators i.e. for 7758,9618 is 6
LCM of denominators i.e. for 408,9752 is 497352.
Thus, GCF of Fractions is 6/497352.Finally, GCF of Fractions for 7758/408, 9618/9752 is 6/497352.