GCF of 5705/618, 6420/8284
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 5705/618, 6420/8284 i.e 5/2559756 easily. The following is the detailed procedure to determine the greatest common factor of fractions 5705/618, 6420/8284.
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 5705/618,6420/8284?
Given fractions are 5705/618,6420/8284
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 5705/618,6420/8284, numerators are 5705,6420
Denominators are 618,8284
The GCF of 5705,6420 is 5 .
LCM of 618,8284 is 2559756.
The greatest common factor of 5705/618,6420/8284 = [GCF of 5705,6420]/[LCM of 618,8284]= 5/2559756
Therefore, the GCF of 5705/618,6420/8284 is 5/2559756.
To find the highest common factor of 5705,6420, we have to find the factors of both numbers and list the highest common factor.
The factors of 5705 are 1, 5, 7, 35, 163, 815, 1141, 5705
The factors of 6420 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60, 107, 214, 321, 428, 535, 642, 1070, 1284, 1605, 2140, 3210, 6420
The HCF of 5705,6420 is 5.
Lets's calculate GCF of 5705,6420
| 5 | 5705, 6420 |
| 1141, 1284 |
∴ So the GCF of the given numbers is 5 = 5
Greatest Common Factor of 5705,6420 By Matching Biggest Common Factor Method
Now, list down the factors of 5705
:1,5,7,35,163,815,1141,5705
Now, list down the factors of 6420
:1,2,3,4,5,6,10,12,15,20,30,60,107,214,321,428,535,642,1070,1284,1605,2140,3210,6420
Greatest Common Factor
We found the factors 5705,6420 . The biggest common factor number is the GCF number.
So the greatest common factor 5705,6420 is 5.
Lets's calculate LCM of 618,8284
| 2 | 618, 8284 |
| 309, 4142 |
∴ So the LCM of the given numbers is 2 x 309 x 4142 = 2559756
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 5/2559756
Therefore, the GCF of Fractions 5705/618,6420/8284 is 5/2559756
Least Common Multiple of 618,8284 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 618,8284 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(618,8284) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(618,8284) x common factors =2 x 1 = 2
LCM(618,8284) = ( 618 × 8284 ) / 2
LCM(618,8284) = 5119512 / 2
LCM(618,8284) = 2559756
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FAQs on GCF of Fractions of 5705/618, 6420/8284
1. What is the HCF of 5705,6420?
The HCF of 5705,6420 is 5
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 5705/618, 6420/8284?
Answer: GCF of Numerators as per given numbers 5705/618, 6420/8284 is
GCF of Numerators i.e. for 5705,6420 is 5
LCM of denominators i.e. for 618,8284 is 2559756.
Thus, GCF of Fractions is 5/2559756.Finally, GCF of Fractions for 5705/618, 6420/8284 is 5/2559756.