GCF of 8274/354, 5625/723
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 8274/354, 5625/723 i.e 3/85314 easily. The following is the detailed procedure to determine the greatest common factor of fractions 8274/354, 5625/723.
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 8274/354,5625/723?
Given fractions are 8274/354,5625/723
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 8274/354,5625/723, numerators are 8274,5625
Denominators are 354,723
The GCF of 8274,5625 is 3 .
LCM of 354,723 is 85314.
The greatest common factor of 8274/354,5625/723 = [GCF of 8274,5625]/[LCM of 354,723]= 3/85314
Therefore, the GCF of 8274/354,5625/723 is 3/85314.
To find the highest common factor of 8274,5625, we have to find the factors of both numbers and list the highest common factor.
The factors of 8274 are 1, 2, 3, 6, 7, 14, 21, 42, 197, 394, 591, 1182, 1379, 2758, 4137, 8274
The factors of 5625 are 1, 3, 5, 9, 15, 25, 45, 75, 125, 225, 375, 625, 1125, 1875, 5625
The HCF of 8274,5625 is 3.
Lets's calculate GCF of 8274,5625
| 3 | 8274, 5625 |
| 2758, 1875 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 8274,5625 By Matching Biggest Common Factor Method
Now, list down the factors of 8274
:1,2,3,6,7,14,21,42,197,394,591,1182,1379,2758,4137,8274
Now, list down the factors of 5625
:1,3,5,9,15,25,45,75,125,225,375,625,1125,1875,5625
Greatest Common Factor
We found the factors 8274,5625 . The biggest common factor number is the GCF number.
So the greatest common factor 8274,5625 is 3.
Lets's calculate LCM of 354,723
| 3 | 354, 723 |
| 118, 241 |
∴ So the LCM of the given numbers is 3 x 118 x 241 = 85314
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/85314
Therefore, the GCF of Fractions 8274/354,5625/723 is 3/85314
Least Common Multiple of 354,723 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 354,723 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(354,723) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(354,723) x common factors =3 x 1 = 3
LCM(354,723) = ( 354 × 723 ) / 3
LCM(354,723) = 255942 / 3
LCM(354,723) = 85314
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FAQs on GCF of Fractions of 8274/354, 5625/723
1. What is the HCF of 8274,5625?
The HCF of 8274,5625 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 8274/354, 5625/723?
Answer: GCF of Numerators as per given numbers 8274/354, 5625/723 is
GCF of Numerators i.e. for 8274,5625 is 3
LCM of denominators i.e. for 354,723 is 85314.
Thus, GCF of Fractions is 3/85314.Finally, GCF of Fractions for 8274/354, 5625/723 is 3/85314.