GCF of 7874/420, 1734/4774
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 7874/420, 1734/4774 i.e 2/143220 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7874/420, 1734/4774.
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 7874/420,1734/4774?
Given fractions are 7874/420,1734/4774
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 7874/420,1734/4774, numerators are 7874,1734
Denominators are 420,4774
The GCF of 7874,1734 is 2 .
LCM of 420,4774 is 143220.
The greatest common factor of 7874/420,1734/4774 = [GCF of 7874,1734]/[LCM of 420,4774]= 2/143220
Therefore, the GCF of 7874/420,1734/4774 is 2/143220.
To find the highest common factor of 7874,1734, we have to find the factors of both numbers and list the highest common factor.
The factors of 7874 are 1, 2, 31, 62, 127, 254, 3937, 7874
The factors of 1734 are 1, 2, 3, 6, 17, 34, 51, 102, 289, 578, 867, 1734
The HCF of 7874,1734 is 2.
Lets's calculate GCF of 7874,1734
| 2 | 7874, 1734 |
| 3937, 867 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 7874,1734 By Matching Biggest Common Factor Method
Now, list down the factors of 7874
:1,2,31,62,127,254,3937,7874
Now, list down the factors of 1734
:1,2,3,6,17,34,51,102,289,578,867,1734
Greatest Common Factor
We found the factors 7874,1734 . The biggest common factor number is the GCF number.
So the greatest common factor 7874,1734 is 2.
Lets's calculate LCM of 420,4774
| 2 | 420, 4774 |
| 7 | 210, 2387 |
| 30, 341 |
∴ So the LCM of the given numbers is 2 x 7 x 30 x 341 = 143220
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/143220
Therefore, the GCF of Fractions 7874/420,1734/4774 is 2/143220
Least Common Multiple of 420,4774 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 420,4774 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(420,4774) = 14
common factors(in case of two or more numbers have common factors) = 1
GCF(420,4774) x common factors =14 x 1 = 14
LCM(420,4774) = ( 420 × 4774 ) / 14
LCM(420,4774) = 2005080 / 14
LCM(420,4774) = 143220
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FAQs on GCF of Fractions of 7874/420, 1734/4774
1. What is the HCF of 7874,1734?
The HCF of 7874,1734 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 7874/420, 1734/4774?
Answer: GCF of Numerators as per given numbers 7874/420, 1734/4774 is
GCF of Numerators i.e. for 7874,1734 is 2
LCM of denominators i.e. for 420,4774 is 143220.
Thus, GCF of Fractions is 2/143220.Finally, GCF of Fractions for 7874/420, 1734/4774 is 2/143220.