GCF of 838/64, 414/1672
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 838/64, 414/1672 i.e 2/13376 easily. The following is the detailed procedure to determine the greatest common factor of fractions 838/64, 414/1672.
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 838/64,414/1672?
Given fractions are 838/64,414/1672
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 838/64,414/1672, numerators are 838,414
Denominators are 64,1672
The GCF of 838,414 is 2 .
LCM of 64,1672 is 13376.
The greatest common factor of 838/64,414/1672 = [GCF of 838,414]/[LCM of 64,1672]= 2/13376
Therefore, the GCF of 838/64,414/1672 is 2/13376.
To find the highest common factor of 838,414, we have to find the factors of both numbers and list the highest common factor.
The factors of 838 are 1, 2, 419, 838
The factors of 414 are 1, 2, 3, 6, 9, 18, 23, 46, 69, 138, 207, 414
The HCF of 838,414 is 2.
Lets's calculate GCF of 838,414
| 2 | 838, 414 |
| 419, 207 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 838,414 By Matching Biggest Common Factor Method
Now, list down the factors of 838
:1,2,419,838
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 838,414 . The biggest common factor number is the GCF number.
So the greatest common factor 838,414 is 2.
Lets's calculate LCM of 64,1672
| 2 | 64, 1672 |
| 2 | 32, 836 |
| 2 | 16, 418 |
| 8, 209 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 8 x 209 = 13376
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/13376
Therefore, the GCF of Fractions 838/64,414/1672 is 2/13376
Least Common Multiple of 64,1672 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 64,1672 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(64,1672) = 8
common factors(in case of two or more numbers have common factors) = 1
GCF(64,1672) x common factors =8 x 1 = 8
LCM(64,1672) = ( 64 × 1672 ) / 8
LCM(64,1672) = 107008 / 8
LCM(64,1672) = 13376
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FAQs on GCF of Fractions of 838/64, 414/1672
1. What is the HCF of 838,414?
The HCF of 838,414 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 838/64, 414/1672?
Answer: GCF of Numerators as per given numbers 838/64, 414/1672 is
GCF of Numerators i.e. for 838,414 is 2
LCM of denominators i.e. for 64,1672 is 13376.
Thus, GCF of Fractions is 2/13376.Finally, GCF of Fractions for 838/64, 414/1672 is 2/13376.