GCF of 344/58, 709/1330
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 344/58, 709/1330 i.e 1/38570 easily. The following is the detailed procedure to determine the greatest common factor of fractions 344/58, 709/1330.
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 344/58,709/1330?
Given fractions are 344/58,709/1330
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 344/58,709/1330, numerators are 344,709
Denominators are 58,1330
The GCF of 344,709 is 1 .
LCM of 58,1330 is 38570.
The greatest common factor of 344/58,709/1330 = [GCF of 344,709]/[LCM of 58,1330]= 1/38570
Therefore, the GCF of 344/58,709/1330 is 1/38570.
To find the highest common factor of 344,709, we have to find the factors of both numbers and list the highest common factor.
The factors of 344 are 1, 2, 4, 8, 43, 86, 172, 344
The factors of 709 are 1, 709
The HCF of 344,709 is 1.
Lets's calculate GCF of 344,709
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 344,709 By Matching Biggest Common Factor Method
Now, list down the factors of 344
:1,2,4,8,43,86,172,344
Now, list down the factors of 709
:1,709
Greatest Common Factor
We found the factors 344,709 . The biggest common factor number is the GCF number.
So the greatest common factor 344,709 is 1.
Lets's calculate LCM of 58,1330
| 2 | 58, 1330 |
| 29, 665 |
∴ So the LCM of the given numbers is 2 x 29 x 665 = 38570
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/38570
Therefore, the GCF of Fractions 344/58,709/1330 is 1/38570
Least Common Multiple of 58,1330 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 58,1330 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(58,1330) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(58,1330) x common factors =2 x 1 = 2
LCM(58,1330) = ( 58 × 1330 ) / 2
LCM(58,1330) = 77140 / 2
LCM(58,1330) = 38570
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FAQs on GCF of Fractions of 344/58, 709/1330
1. What is the HCF of 344,709?
The HCF of 344,709 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 344/58, 709/1330?
Answer: GCF of Numerators as per given numbers 344/58, 709/1330 is
GCF of Numerators i.e. for 344,709 is 1
LCM of denominators i.e. for 58,1330 is 38570.
Thus, GCF of Fractions is 1/38570.Finally, GCF of Fractions for 344/58, 709/1330 is 1/38570.