GCF of 5780/103, 8920/9957
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 5780/103, 8920/9957 i.e 20/1025571 easily. The following is the detailed procedure to determine the greatest common factor of fractions 5780/103, 8920/9957.
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 5780/103,8920/9957?
Given fractions are 5780/103,8920/9957
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 5780/103,8920/9957, numerators are 5780,8920
Denominators are 103,9957
The GCF of 5780,8920 is 20 .
LCM of 103,9957 is 1025571.
The greatest common factor of 5780/103,8920/9957 = [GCF of 5780,8920]/[LCM of 103,9957]= 20/1025571
Therefore, the GCF of 5780/103,8920/9957 is 20/1025571.
To find the highest common factor of 5780,8920, we have to find the factors of both numbers and list the highest common factor.
The factors of 5780 are 1, 2, 4, 5, 10, 17, 20, 34, 68, 85, 170, 289, 340, 578, 1156, 1445, 2890, 5780
The factors of 8920 are 1, 2, 4, 5, 8, 10, 20, 40, 223, 446, 892, 1115, 1784, 2230, 4460, 8920
The HCF of 5780,8920 is 20.
Lets's calculate GCF of 5780,8920
| 2 | 5780, 8920 |
| 2 | 2890, 4460 |
| 5 | 1445, 2230 |
| 289, 446 |
∴ So the GCF of the given numbers is 2 x 2 x 5 = 20
Greatest Common Factor of 5780,8920 By Matching Biggest Common Factor Method
Now, list down the factors of 5780
:1,2,4,5,10,17,20,34,68,85,170,289,340,578,1156,1445,2890,5780
Now, list down the factors of 8920
:1,2,4,5,8,10,20,40,223,446,892,1115,1784,2230,4460,8920
Greatest Common Factor
We found the factors 5780,8920 . The biggest common factor number is the GCF number.
So the greatest common factor 5780,8920 is 20.
Lets's calculate LCM of 103,9957
Given numbers has no common factors except 1. So, there LCM is their product i.e 1025571
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 20/1025571
Therefore, the GCF of Fractions 5780/103,8920/9957 is 20/1025571
Least Common Multiple of 103,9957 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 103,9957 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(103,9957) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(103,9957) x common factors =1 x 1 = 1
LCM(103,9957) = ( 103 × 9957 ) / 1
LCM(103,9957) = 1025571 / 1
LCM(103,9957) = 1025571
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FAQs on GCF of Fractions of 5780/103, 8920/9957
1. What is the HCF of 5780,8920?
The HCF of 5780,8920 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 5780/103, 8920/9957?
Answer: GCF of Numerators as per given numbers 5780/103, 8920/9957 is
GCF of Numerators i.e. for 5780,8920 is 20
LCM of denominators i.e. for 103,9957 is 1025571.
Thus, GCF of Fractions is 20/1025571.Finally, GCF of Fractions for 5780/103, 8920/9957 is 20/1025571.