GCF of 723/578, 9675/724
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 723/578, 9675/724 i.e 3/209236 easily. The following is the detailed procedure to determine the greatest common factor of fractions 723/578, 9675/724.
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 723/578,9675/724?
Given fractions are 723/578,9675/724
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 723/578,9675/724, numerators are 723,9675
Denominators are 578,724
The GCF of 723,9675 is 3 .
LCM of 578,724 is 209236.
The greatest common factor of 723/578,9675/724 = [GCF of 723,9675]/[LCM of 578,724]= 3/209236
Therefore, the GCF of 723/578,9675/724 is 3/209236.
To find the highest common factor of 723,9675, we have to find the factors of both numbers and list the highest common factor.
The factors of 723 are 1, 3, 241, 723
The factors of 9675 are 1, 3, 5, 9, 15, 25, 43, 45, 75, 129, 215, 225, 387, 645, 1075, 1935, 3225, 9675
The HCF of 723,9675 is 3.
Lets's calculate GCF of 723,9675
| 3 | 723, 9675 |
| 241, 3225 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 723,9675 By Matching Biggest Common Factor Method
Now, list down the factors of 723
:1,3,241,723
Now, list down the factors of 9675
:1,3,5,9,15,25,43,45,75,129,215,225,387,645,1075,1935,3225,9675
Greatest Common Factor
We found the factors 723,9675 . The biggest common factor number is the GCF number.
So the greatest common factor 723,9675 is 3.
Lets's calculate LCM of 578,724
| 2 | 578, 724 |
| 289, 362 |
∴ So the LCM of the given numbers is 2 x 289 x 362 = 209236
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/209236
Therefore, the GCF of Fractions 723/578,9675/724 is 3/209236
Least Common Multiple of 578,724 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 578,724 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(578,724) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(578,724) x common factors =2 x 1 = 2
LCM(578,724) = ( 578 × 724 ) / 2
LCM(578,724) = 418472 / 2
LCM(578,724) = 209236
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FAQs on GCF of Fractions of 723/578, 9675/724
1. What is the HCF of 723,9675?
The HCF of 723,9675 is 3
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 723/578, 9675/724?
Answer: GCF of Numerators as per given numbers 723/578, 9675/724 is
GCF of Numerators i.e. for 723,9675 is 3
LCM of denominators i.e. for 578,724 is 209236.
Thus, GCF of Fractions is 3/209236.Finally, GCF of Fractions for 723/578, 9675/724 is 3/209236.