GCF of 4120/782, 8717/7114
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 4120/782, 8717/7114 i.e 1/2781574 easily. The following is the detailed procedure to determine the greatest common factor of fractions 4120/782, 8717/7114.
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 4120/782,8717/7114?
Given fractions are 4120/782,8717/7114
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 4120/782,8717/7114, numerators are 4120,8717
Denominators are 782,7114
The GCF of 4120,8717 is 1 .
LCM of 782,7114 is 2781574.
The greatest common factor of 4120/782,8717/7114 = [GCF of 4120,8717]/[LCM of 782,7114]= 1/2781574
Therefore, the GCF of 4120/782,8717/7114 is 1/2781574.
To find the highest common factor of 4120,8717, we have to find the factors of both numbers and list the highest common factor.
The factors of 4120 are 1, 2, 4, 5, 8, 10, 20, 40, 103, 206, 412, 515, 824, 1030, 2060, 4120
The factors of 8717 are 1, 23, 379, 8717
The HCF of 4120,8717 is 1.
Lets's calculate GCF of 4120,8717
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 4120,8717 By Matching Biggest Common Factor Method
Now, list down the factors of 4120
:1,2,4,5,8,10,20,40,103,206,412,515,824,1030,2060,4120
Now, list down the factors of 8717
:1,23,379,8717
Greatest Common Factor
We found the factors 4120,8717 . The biggest common factor number is the GCF number.
So the greatest common factor 4120,8717 is 1.
Lets's calculate LCM of 782,7114
| 2 | 782, 7114 |
| 391, 3557 |
∴ So the LCM of the given numbers is 2 x 391 x 3557 = 2781574
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/2781574
Therefore, the GCF of Fractions 4120/782,8717/7114 is 1/2781574
Least Common Multiple of 782,7114 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 782,7114 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(782,7114) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(782,7114) x common factors =2 x 1 = 2
LCM(782,7114) = ( 782 × 7114 ) / 2
LCM(782,7114) = 5563148 / 2
LCM(782,7114) = 2781574
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FAQs on GCF of Fractions of 4120/782, 8717/7114
1. What is the HCF of 4120,8717?
The HCF of 4120,8717 is 1
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 4120/782, 8717/7114?
Answer: GCF of Numerators as per given numbers 4120/782, 8717/7114 is
GCF of Numerators i.e. for 4120,8717 is 1
LCM of denominators i.e. for 782,7114 is 2781574.
Thus, GCF of Fractions is 1/2781574.Finally, GCF of Fractions for 4120/782, 8717/7114 is 1/2781574.