GCF of 9780/760, 5180/556
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 9780/760, 5180/556 i.e 20/105640 easily. The following is the detailed procedure to determine the greatest common factor of fractions 9780/760, 5180/556.
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 9780/760,5180/556?
Given fractions are 9780/760,5180/556
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 9780/760,5180/556, numerators are 9780,5180
Denominators are 760,556
The GCF of 9780,5180 is 20 .
LCM of 760,556 is 105640.
The greatest common factor of 9780/760,5180/556 = [GCF of 9780,5180]/[LCM of 760,556]= 20/105640
Therefore, the GCF of 9780/760,5180/556 is 20/105640.
To find the highest common factor of 9780,5180, we have to find the factors of both numbers and list the highest common factor.
The factors of 9780 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60, 163, 326, 489, 652, 815, 978, 1630, 1956, 2445, 3260, 4890, 9780
The factors of 5180 are 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 37, 70, 74, 140, 148, 185, 259, 370, 518, 740, 1036, 1295, 2590, 5180
The HCF of 9780,5180 is 20.
Lets's calculate GCF of 9780,5180
| 2 | 9780, 5180 |
| 2 | 4890, 2590 |
| 5 | 2445, 1295 |
| 489, 259 |
∴ So the GCF of the given numbers is 2 x 2 x 5 = 20
Greatest Common Factor of 9780,5180 By Matching Biggest Common Factor Method
Now, list down the factors of 9780
:1,2,3,4,5,6,10,12,15,20,30,60,163,326,489,652,815,978,1630,1956,2445,3260,4890,9780
Now, list down the factors of 5180
:1,2,4,5,7,10,14,20,28,35,37,70,74,140,148,185,259,370,518,740,1036,1295,2590,5180
Greatest Common Factor
We found the factors 9780,5180 . The biggest common factor number is the GCF number.
So the greatest common factor 9780,5180 is 20.
Lets's calculate LCM of 760,556
| 2 | 760, 556 |
| 2 | 380, 278 |
| 190, 139 |
∴ So the LCM of the given numbers is 2 x 2 x 190 x 139 = 105640
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 20/105640
Therefore, the GCF of Fractions 9780/760,5180/556 is 20/105640
Least Common Multiple of 760,556 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 760,556 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(760,556) = 4
common factors(in case of two or more numbers have common factors) = 1
GCF(760,556) x common factors =4 x 1 = 4
LCM(760,556) = ( 760 × 556 ) / 4
LCM(760,556) = 422560 / 4
LCM(760,556) = 105640
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FAQs on GCF of Fractions of 9780/760, 5180/556
1. What is the HCF of 9780,5180?
The HCF of 9780,5180 is 20
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 9780/760, 5180/556?
Answer: GCF of Numerators as per given numbers 9780/760, 5180/556 is
GCF of Numerators i.e. for 9780,5180 is 20
LCM of denominators i.e. for 760,556 is 105640.
Thus, GCF of Fractions is 20/105640.Finally, GCF of Fractions for 9780/760, 5180/556 is 20/105640.