GCF of 5106/560, 9078/705
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 5106/560, 9078/705 i.e 6/78960 easily. The following is the detailed procedure to determine the greatest common factor of fractions 5106/560, 9078/705.
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 5106/560,9078/705?
Given fractions are 5106/560,9078/705
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 5106/560,9078/705, numerators are 5106,9078
Denominators are 560,705
The GCF of 5106,9078 is 6 .
LCM of 560,705 is 78960.
The greatest common factor of 5106/560,9078/705 = [GCF of 5106,9078]/[LCM of 560,705]= 6/78960
Therefore, the GCF of 5106/560,9078/705 is 6/78960.
To find the highest common factor of 5106,9078, we have to find the factors of both numbers and list the highest common factor.
The factors of 5106 are 1, 2, 3, 6, 23, 37, 46, 69, 74, 111, 138, 222, 851, 1702, 2553, 5106
The factors of 9078 are 1, 2, 3, 6, 17, 34, 51, 89, 102, 178, 267, 534, 1513, 3026, 4539, 9078
The HCF of 5106,9078 is 6.
Lets's calculate GCF of 5106,9078
| 2 | 5106, 9078 |
| 3 | 2553, 4539 |
| 851, 1513 |
∴ So the GCF of the given numbers is 2 x 3 = 6
Greatest Common Factor of 5106,9078 By Matching Biggest Common Factor Method
Now, list down the factors of 5106
:1,2,3,6,23,37,46,69,74,111,138,222,851,1702,2553,5106
Now, list down the factors of 9078
:1,2,3,6,17,34,51,89,102,178,267,534,1513,3026,4539,9078
Greatest Common Factor
We found the factors 5106,9078 . The biggest common factor number is the GCF number.
So the greatest common factor 5106,9078 is 6.
Lets's calculate LCM of 560,705
| 5 | 560, 705 |
| 112, 141 |
∴ So the LCM of the given numbers is 5 x 112 x 141 = 78960
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/78960
Therefore, the GCF of Fractions 5106/560,9078/705 is 6/78960
Least Common Multiple of 560,705 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 560,705 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(560,705) = 5
common factors(in case of two or more numbers have common factors) = 1
GCF(560,705) x common factors =5 x 1 = 5
LCM(560,705) = ( 560 × 705 ) / 5
LCM(560,705) = 394800 / 5
LCM(560,705) = 78960
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FAQs on GCF of Fractions of 5106/560, 9078/705
1. What is the HCF of 5106,9078?
The HCF of 5106,9078 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 5106/560, 9078/705?
Answer: GCF of Numerators as per given numbers 5106/560, 9078/705 is
GCF of Numerators i.e. for 5106,9078 is 6
LCM of denominators i.e. for 560,705 is 78960.
Thus, GCF of Fractions is 6/78960.Finally, GCF of Fractions for 5106/560, 9078/705 is 6/78960.