GCF of 3471/219, 6880/234
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 3471/219, 6880/234 i.e 1/17082 easily. The following is the detailed procedure to determine the greatest common factor of fractions 3471/219, 6880/234.
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 3471/219,6880/234?
Given fractions are 3471/219,6880/234
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 3471/219,6880/234, numerators are 3471,6880
Denominators are 219,234
The GCF of 3471,6880 is 1 .
LCM of 219,234 is 17082.
The greatest common factor of 3471/219,6880/234 = [GCF of 3471,6880]/[LCM of 219,234]= 1/17082
Therefore, the GCF of 3471/219,6880/234 is 1/17082.
To find the highest common factor of 3471,6880, we have to find the factors of both numbers and list the highest common factor.
The factors of 3471 are 1, 3, 13, 39, 89, 267, 1157, 3471
The factors of 6880 are 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 43, 80, 86, 160, 172, 215, 344, 430, 688, 860, 1376, 1720, 3440, 6880
The HCF of 3471,6880 is 1.
Lets's calculate GCF of 3471,6880
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 3471,6880 By Matching Biggest Common Factor Method
Now, list down the factors of 3471
:1,3,13,39,89,267,1157,3471
Now, list down the factors of 6880
:1,2,4,5,8,10,16,20,32,40,43,80,86,160,172,215,344,430,688,860,1376,1720,3440,6880
Greatest Common Factor
We found the factors 3471,6880 . The biggest common factor number is the GCF number.
So the greatest common factor 3471,6880 is 1.
Lets's calculate LCM of 219,234
| 3 | 219, 234 |
| 73, 78 |
∴ So the LCM of the given numbers is 3 x 73 x 78 = 17082
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/17082
Therefore, the GCF of Fractions 3471/219,6880/234 is 1/17082
Least Common Multiple of 219,234 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 219,234 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(219,234) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(219,234) x common factors =3 x 1 = 3
LCM(219,234) = ( 219 × 234 ) / 3
LCM(219,234) = 51246 / 3
LCM(219,234) = 17082
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FAQs on GCF of Fractions of 3471/219, 6880/234
1. What is the HCF of 3471,6880?
The HCF of 3471,6880 is 1
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 3471/219, 6880/234?
Answer: GCF of Numerators as per given numbers 3471/219, 6880/234 is
GCF of Numerators i.e. for 3471,6880 is 1
LCM of denominators i.e. for 219,234 is 17082.
Thus, GCF of Fractions is 1/17082.Finally, GCF of Fractions for 3471/219, 6880/234 is 1/17082.