GCF of 2719/414, 7070/3004
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 2719/414, 7070/3004 i.e 1/621828 easily. The following is the detailed procedure to determine the greatest common factor of fractions 2719/414, 7070/3004.
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 2719/414,7070/3004?
Given fractions are 2719/414,7070/3004
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 2719/414,7070/3004, numerators are 2719,7070
Denominators are 414,3004
The GCF of 2719,7070 is 1 .
LCM of 414,3004 is 621828.
The greatest common factor of 2719/414,7070/3004 = [GCF of 2719,7070]/[LCM of 414,3004]= 1/621828
Therefore, the GCF of 2719/414,7070/3004 is 1/621828.
To find the highest common factor of 2719,7070, we have to find the factors of both numbers and list the highest common factor.
The factors of 2719 are 1, 2719
The factors of 7070 are 1, 2, 5, 7, 10, 14, 35, 70, 101, 202, 505, 707, 1010, 1414, 3535, 7070
The HCF of 2719,7070 is 1.
Lets's calculate GCF of 2719,7070
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 2719,7070 By Matching Biggest Common Factor Method
Now, list down the factors of 2719
:1,2719
Now, list down the factors of 7070
:1,2,5,7,10,14,35,70,101,202,505,707,1010,1414,3535,7070
Greatest Common Factor
We found the factors 2719,7070 . The biggest common factor number is the GCF number.
So the greatest common factor 2719,7070 is 1.
Lets's calculate LCM of 414,3004
| 2 | 414, 3004 |
| 207, 1502 |
∴ So the LCM of the given numbers is 2 x 207 x 1502 = 621828
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/621828
Therefore, the GCF of Fractions 2719/414,7070/3004 is 1/621828
Least Common Multiple of 414,3004 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 414,3004 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(414,3004) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(414,3004) x common factors =2 x 1 = 2
LCM(414,3004) = ( 414 × 3004 ) / 2
LCM(414,3004) = 1243656 / 2
LCM(414,3004) = 621828
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FAQs on GCF of Fractions of 2719/414, 7070/3004
1. What is the HCF of 2719,7070?
The HCF of 2719,7070 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 2719/414, 7070/3004?
Answer: GCF of Numerators as per given numbers 2719/414, 7070/3004 is
GCF of Numerators i.e. for 2719,7070 is 1
LCM of denominators i.e. for 414,3004 is 621828.
Thus, GCF of Fractions is 1/621828.Finally, GCF of Fractions for 2719/414, 7070/3004 is 1/621828.