GCF of 64/868, 20/417, 105/556
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 64/868, 20/417, 105/556 i.e 1/361956 easily. The following is the detailed procedure to determine the greatest common factor of fractions 64/868, 20/417, 105/556.
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 64/868,20/417,105/556?
Given fractions are 64/868,20/417,105/556
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 64/868,20/417,105/556, numerators are 64,20,105
Denominators are 868,417,556
The GCF of 64,20,105 is 1 .
LCM of 868,417,556 is 361956.
The greatest common factor of 64/868,20/417,105/556 = [GCF of 64,20,105]/[LCM of 868,417,556]= 1/361956
Therefore, the GCF of 64/868,20/417,105/556 is 1/361956.
To find the highest common factor of 64,20,105, we have to find the factors of both numbers and list the highest common factor.
The factors of 64 are 1, 2, 4, 8, 16, 32, 64
The factors of 20 are 1, 2, 4, 5, 10, 20
The factors of 105 are 1, 3, 5, 7, 15, 21, 35, 105
The HCF of 64,20,105 is 1.
Lets's calculate GCF of 64,20,105
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 64,20,105 By Matching Biggest Common Factor Method
Now, list down the factors of 64
:1,2,4,8,16,32,64
Now, list down the factors of 20
:1,2,4,5,10,20
Now, list down the factors of 105
:1,3,5,7,15,21,35,105
Greatest Common Factor
We found the factors 64,20,105 . The biggest common factor number is the GCF number.
So the greatest common factor 64,20,105 is 1.
Lets's calculate LCM of 868,417,556
| 2 | 868, 417, 556 |
| 2 | 434, 417, 278 |
| 139 | 217, 417, 139 |
| 217, 3, 1 |
∴ So the LCM of the given numbers is 2 x 2 x 139 x 217 x 3 x 1 = 361956
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/361956
Therefore, the GCF of Fractions 64/868,20/417,105/556 is 1/361956
Least Common Multiple of 868,417,556 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 868,417,556 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(868,417,556) = 1
common factors(in case of two or more numbers have common factors) = 556
GCF(868,417,556) x common factors =1 x 556 = 556
LCM(868,417,556) = ( 868 × 417 × 556 ) / 556
LCM(868,417,556) = 201247536 / 556
LCM(868,417,556) = 361956
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FAQs on GCF of Fractions of 64/868, 20/417, 105/556
1. What is the HCF of 64,20,105?
The HCF of 64,20,105 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 64/868, 20/417, 105/556?
Answer: GCF of Numerators as per given numbers 64/868, 20/417, 105/556 is
GCF of Numerators i.e. for 64,20,105 is 1
LCM of denominators i.e. for 868,417,556 is 361956.
Thus, GCF of Fractions is 1/361956.Finally, GCF of Fractions for 64/868, 20/417, 105/556 is 1/361956.