GCF of 230/75, 688/578
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 230/75, 688/578 i.e 2/43350 easily. The following is the detailed procedure to determine the greatest common factor of fractions 230/75, 688/578.
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 230/75,688/578?
Given fractions are 230/75,688/578
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 230/75,688/578, numerators are 230,688
Denominators are 75,578
The GCF of 230,688 is 2 .
LCM of 75,578 is 43350.
The greatest common factor of 230/75,688/578 = [GCF of 230,688]/[LCM of 75,578]= 2/43350
Therefore, the GCF of 230/75,688/578 is 2/43350.
To find the highest common factor of 230,688, we have to find the factors of both numbers and list the highest common factor.
The factors of 230 are 1, 2, 5, 10, 23, 46, 115, 230
The factors of 688 are 1, 2, 4, 8, 16, 43, 86, 172, 344, 688
The HCF of 230,688 is 2.
Lets's calculate GCF of 230,688
| 2 | 230, 688 |
| 115, 344 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 230,688 By Matching Biggest Common Factor Method
Now, list down the factors of 230
:1,2,5,10,23,46,115,230
Now, list down the factors of 688
:1,2,4,8,16,43,86,172,344,688
Greatest Common Factor
We found the factors 230,688 . The biggest common factor number is the GCF number.
So the greatest common factor 230,688 is 2.
Lets's calculate LCM of 75,578
Given numbers has no common factors except 1. So, there LCM is their product i.e 43350
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/43350
Therefore, the GCF of Fractions 230/75,688/578 is 2/43350
Least Common Multiple of 75,578 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 75,578 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(75,578) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(75,578) x common factors =1 x 1 = 1
LCM(75,578) = ( 75 × 578 ) / 1
LCM(75,578) = 43350 / 1
LCM(75,578) = 43350
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FAQs on GCF of Fractions of 230/75, 688/578
1. What is the HCF of 230,688?
The HCF of 230,688 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 230/75, 688/578?
Answer: GCF of Numerators as per given numbers 230/75, 688/578 is
GCF of Numerators i.e. for 230,688 is 2
LCM of denominators i.e. for 75,578 is 43350.
Thus, GCF of Fractions is 2/43350.Finally, GCF of Fractions for 230/75, 688/578 is 2/43350.