GCF of 9784/574, 1780/9224
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 9784/574, 1780/9224 i.e 4/2647288 easily. The following is the detailed procedure to determine the greatest common factor of fractions 9784/574, 1780/9224.
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 9784/574,1780/9224?
Given fractions are 9784/574,1780/9224
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 9784/574,1780/9224, numerators are 9784,1780
Denominators are 574,9224
The GCF of 9784,1780 is 4 .
LCM of 574,9224 is 2647288.
The greatest common factor of 9784/574,1780/9224 = [GCF of 9784,1780]/[LCM of 574,9224]= 4/2647288
Therefore, the GCF of 9784/574,1780/9224 is 4/2647288.
To find the highest common factor of 9784,1780, we have to find the factors of both numbers and list the highest common factor.
The factors of 9784 are 1, 2, 4, 8, 1223, 2446, 4892, 9784
The factors of 1780 are 1, 2, 4, 5, 10, 20, 89, 178, 356, 445, 890, 1780
The HCF of 9784,1780 is 4.
Lets's calculate GCF of 9784,1780
| 2 | 9784, 1780 |
| 2 | 4892, 890 |
| 2446, 445 |
∴ So the GCF of the given numbers is 2 x 2 = 4
Greatest Common Factor of 9784,1780 By Matching Biggest Common Factor Method
Now, list down the factors of 9784
:1,2,4,8,1223,2446,4892,9784
Now, list down the factors of 1780
:1,2,4,5,10,20,89,178,356,445,890,1780
Greatest Common Factor
We found the factors 9784,1780 . The biggest common factor number is the GCF number.
So the greatest common factor 9784,1780 is 4.
Lets's calculate LCM of 574,9224
| 2 | 574, 9224 |
| 287, 4612 |
∴ So the LCM of the given numbers is 2 x 287 x 4612 = 2647288
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/2647288
Therefore, the GCF of Fractions 9784/574,1780/9224 is 4/2647288
Least Common Multiple of 574,9224 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 574,9224 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(574,9224) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(574,9224) x common factors =2 x 1 = 2
LCM(574,9224) = ( 574 × 9224 ) / 2
LCM(574,9224) = 5294576 / 2
LCM(574,9224) = 2647288
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FAQs on GCF of Fractions of 9784/574, 1780/9224
1. What is the HCF of 9784,1780?
The HCF of 9784,1780 is 4
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 9784/574, 1780/9224?
Answer: GCF of Numerators as per given numbers 9784/574, 1780/9224 is
GCF of Numerators i.e. for 9784,1780 is 4
LCM of denominators i.e. for 574,9224 is 2647288.
Thus, GCF of Fractions is 4/2647288.Finally, GCF of Fractions for 9784/574, 1780/9224 is 4/2647288.