GCF of 762/384, 414/259
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 762/384, 414/259 i.e 6/99456 easily. The following is the detailed procedure to determine the greatest common factor of fractions 762/384, 414/259.
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 762/384,414/259?
Given fractions are 762/384,414/259
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 762/384,414/259, numerators are 762,414
Denominators are 384,259
The GCF of 762,414 is 6 .
LCM of 384,259 is 99456.
The greatest common factor of 762/384,414/259 = [GCF of 762,414]/[LCM of 384,259]= 6/99456
Therefore, the GCF of 762/384,414/259 is 6/99456.
To find the highest common factor of 762,414, we have to find the factors of both numbers and list the highest common factor.
The factors of 762 are 1, 2, 3, 6, 127, 254, 381, 762
The factors of 414 are 1, 2, 3, 6, 9, 18, 23, 46, 69, 138, 207, 414
The HCF of 762,414 is 6.
Lets's calculate GCF of 762,414
| 2 | 762, 414 |
| 3 | 381, 207 |
| 127, 69 |
∴ So the GCF of the given numbers is 2 x 3 = 6
Greatest Common Factor of 762,414 By Matching Biggest Common Factor Method
Now, list down the factors of 762
:1,2,3,6,127,254,381,762
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 762,414 . The biggest common factor number is the GCF number.
So the greatest common factor 762,414 is 6.
Lets's calculate LCM of 384,259
Given numbers has no common factors except 1. So, there LCM is their product i.e 99456
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/99456
Therefore, the GCF of Fractions 762/384,414/259 is 6/99456
Least Common Multiple of 384,259 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 384,259 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(384,259) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(384,259) x common factors =1 x 1 = 1
LCM(384,259) = ( 384 × 259 ) / 1
LCM(384,259) = 99456 / 1
LCM(384,259) = 99456
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FAQs on GCF of Fractions of 762/384, 414/259
1. What is the HCF of 762,414?
The HCF of 762,414 is 6
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 762/384, 414/259?
Answer: GCF of Numerators as per given numbers 762/384, 414/259 is
GCF of Numerators i.e. for 762,414 is 6
LCM of denominators i.e. for 384,259 is 99456.
Thus, GCF of Fractions is 6/99456.Finally, GCF of Fractions for 762/384, 414/259 is 6/99456.