GCF of 3723/840, 8454/1780
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 3723/840, 8454/1780 i.e 3/74760 easily. The following is the detailed procedure to determine the greatest common factor of fractions 3723/840, 8454/1780.
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 3723/840,8454/1780?
Given fractions are 3723/840,8454/1780
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 3723/840,8454/1780, numerators are 3723,8454
Denominators are 840,1780
The GCF of 3723,8454 is 3 .
LCM of 840,1780 is 74760.
The greatest common factor of 3723/840,8454/1780 = [GCF of 3723,8454]/[LCM of 840,1780]= 3/74760
Therefore, the GCF of 3723/840,8454/1780 is 3/74760.
To find the highest common factor of 3723,8454, we have to find the factors of both numbers and list the highest common factor.
The factors of 3723 are 1, 3, 17, 51, 73, 219, 1241, 3723
The factors of 8454 are 1, 2, 3, 6, 1409, 2818, 4227, 8454
The HCF of 3723,8454 is 3.
Lets's calculate GCF of 3723,8454
| 3 | 3723, 8454 |
| 1241, 2818 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 3723,8454 By Matching Biggest Common Factor Method
Now, list down the factors of 3723
:1,3,17,51,73,219,1241,3723
Now, list down the factors of 8454
:1,2,3,6,1409,2818,4227,8454
Greatest Common Factor
We found the factors 3723,8454 . The biggest common factor number is the GCF number.
So the greatest common factor 3723,8454 is 3.
Lets's calculate LCM of 840,1780
| 2 | 840, 1780 |
| 2 | 420, 890 |
| 5 | 210, 445 |
| 42, 89 |
∴ So the LCM of the given numbers is 2 x 2 x 5 x 42 x 89 = 74760
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/74760
Therefore, the GCF of Fractions 3723/840,8454/1780 is 3/74760
Least Common Multiple of 840,1780 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 840,1780 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(840,1780) = 20
common factors(in case of two or more numbers have common factors) = 1
GCF(840,1780) x common factors =20 x 1 = 20
LCM(840,1780) = ( 840 × 1780 ) / 20
LCM(840,1780) = 1495200 / 20
LCM(840,1780) = 74760
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FAQs on GCF of Fractions of 3723/840, 8454/1780
1. What is the HCF of 3723,8454?
The HCF of 3723,8454 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 3723/840, 8454/1780?
Answer: GCF of Numerators as per given numbers 3723/840, 8454/1780 is
GCF of Numerators i.e. for 3723,8454 is 3
LCM of denominators i.e. for 840,1780 is 74760.
Thus, GCF of Fractions is 3/74760.Finally, GCF of Fractions for 3723/840, 8454/1780 is 3/74760.