GCF of 568/14, 214/875
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 568/14, 214/875 i.e 2/1750 easily. The following is the detailed procedure to determine the greatest common factor of fractions 568/14, 214/875.
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 568/14,214/875?
Given fractions are 568/14,214/875
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 568/14,214/875, numerators are 568,214
Denominators are 14,875
The GCF of 568,214 is 2 .
LCM of 14,875 is 1750.
The greatest common factor of 568/14,214/875 = [GCF of 568,214]/[LCM of 14,875]= 2/1750
Therefore, the GCF of 568/14,214/875 is 2/1750.
To find the highest common factor of 568,214, we have to find the factors of both numbers and list the highest common factor.
The factors of 568 are 1, 2, 4, 8, 71, 142, 284, 568
The factors of 214 are 1, 2, 107, 214
The HCF of 568,214 is 2.
Lets's calculate GCF of 568,214
| 2 | 568, 214 |
| 284, 107 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 568,214 By Matching Biggest Common Factor Method
Now, list down the factors of 568
:1,2,4,8,71,142,284,568
Now, list down the factors of 214
:1,2,107,214
Greatest Common Factor
We found the factors 568,214 . The biggest common factor number is the GCF number.
So the greatest common factor 568,214 is 2.
Lets's calculate LCM of 14,875
| 7 | 14, 875 |
| 2, 125 |
∴ So the LCM of the given numbers is 7 x 2 x 125 = 1750
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/1750
Therefore, the GCF of Fractions 568/14,214/875 is 2/1750
Least Common Multiple of 14,875 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 14,875 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(14,875) = 7
common factors(in case of two or more numbers have common factors) = 1
GCF(14,875) x common factors =7 x 1 = 7
LCM(14,875) = ( 14 × 875 ) / 7
LCM(14,875) = 12250 / 7
LCM(14,875) = 1750
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FAQs on GCF of Fractions of 568/14, 214/875
1. What is the HCF of 568,214?
The HCF of 568,214 is 2
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 568/14, 214/875?
Answer: GCF of Numerators as per given numbers 568/14, 214/875 is
GCF of Numerators i.e. for 568,214 is 2
LCM of denominators i.e. for 14,875 is 1750.
Thus, GCF of Fractions is 2/1750.Finally, GCF of Fractions for 568/14, 214/875 is 2/1750.