GCF of 514/76, 832/414
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 514/76, 832/414 i.e 2/15732 easily. The following is the detailed procedure to determine the greatest common factor of fractions 514/76, 832/414.
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 514/76,832/414?
Given fractions are 514/76,832/414
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 514/76,832/414, numerators are 514,832
Denominators are 76,414
The GCF of 514,832 is 2 .
LCM of 76,414 is 15732.
The greatest common factor of 514/76,832/414 = [GCF of 514,832]/[LCM of 76,414]= 2/15732
Therefore, the GCF of 514/76,832/414 is 2/15732.
To find the highest common factor of 514,832, we have to find the factors of both numbers and list the highest common factor.
The factors of 514 are 1, 2, 257, 514
The factors of 832 are 1, 2, 4, 8, 13, 16, 26, 32, 52, 64, 104, 208, 416, 832
The HCF of 514,832 is 2.
Lets's calculate GCF of 514,832
| 2 | 514, 832 |
| 257, 416 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 514,832 By Matching Biggest Common Factor Method
Now, list down the factors of 514
:1,2,257,514
Now, list down the factors of 832
:1,2,4,8,13,16,26,32,52,64,104,208,416,832
Greatest Common Factor
We found the factors 514,832 . The biggest common factor number is the GCF number.
So the greatest common factor 514,832 is 2.
Lets's calculate LCM of 76,414
| 2 | 76, 414 |
| 38, 207 |
∴ So the LCM of the given numbers is 2 x 38 x 207 = 15732
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/15732
Therefore, the GCF of Fractions 514/76,832/414 is 2/15732
Least Common Multiple of 76,414 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 76,414 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(76,414) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(76,414) x common factors =2 x 1 = 2
LCM(76,414) = ( 76 × 414 ) / 2
LCM(76,414) = 31464 / 2
LCM(76,414) = 15732
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FAQs on GCF of Fractions of 514/76, 832/414
1. What is the HCF of 514,832?
The HCF of 514,832 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 514/76, 832/414?
Answer: GCF of Numerators as per given numbers 514/76, 832/414 is
GCF of Numerators i.e. for 514,832 is 2
LCM of denominators i.e. for 76,414 is 15732.
Thus, GCF of Fractions is 2/15732.Finally, GCF of Fractions for 514/76, 832/414 is 2/15732.