GCF of 614/34, 414/316
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 614/34, 414/316 i.e 2/5372 easily. The following is the detailed procedure to determine the greatest common factor of fractions 614/34, 414/316.
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 614/34,414/316?
Given fractions are 614/34,414/316
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 614/34,414/316, numerators are 614,414
Denominators are 34,316
The GCF of 614,414 is 2 .
LCM of 34,316 is 5372.
The greatest common factor of 614/34,414/316 = [GCF of 614,414]/[LCM of 34,316]= 2/5372
Therefore, the GCF of 614/34,414/316 is 2/5372.
To find the highest common factor of 614,414, we have to find the factors of both numbers and list the highest common factor.
The factors of 614 are 1, 2, 307, 614
The factors of 414 are 1, 2, 3, 6, 9, 18, 23, 46, 69, 138, 207, 414
The HCF of 614,414 is 2.
Lets's calculate GCF of 614,414
| 2 | 614, 414 |
| 307, 207 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 614,414 By Matching Biggest Common Factor Method
Now, list down the factors of 614
:1,2,307,614
Now, list down the factors of 414
:1,2,3,6,9,18,23,46,69,138,207,414
Greatest Common Factor
We found the factors 614,414 . The biggest common factor number is the GCF number.
So the greatest common factor 614,414 is 2.
Lets's calculate LCM of 34,316
| 2 | 34, 316 |
| 17, 158 |
∴ So the LCM of the given numbers is 2 x 17 x 158 = 5372
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/5372
Therefore, the GCF of Fractions 614/34,414/316 is 2/5372
Least Common Multiple of 34,316 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 34,316 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(34,316) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(34,316) x common factors =2 x 1 = 2
LCM(34,316) = ( 34 × 316 ) / 2
LCM(34,316) = 10744 / 2
LCM(34,316) = 5372
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FAQs on GCF of Fractions of 614/34, 414/316
1. What is the HCF of 614,414?
The HCF of 614,414 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 614/34, 414/316?
Answer: GCF of Numerators as per given numbers 614/34, 414/316 is
GCF of Numerators i.e. for 614,414 is 2
LCM of denominators i.e. for 34,316 is 5372.
Thus, GCF of Fractions is 2/5372.Finally, GCF of Fractions for 614/34, 414/316 is 2/5372.