GCF of 322/674, 414/766
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 322/674, 414/766 i.e 46/258142 easily. The following is the detailed procedure to determine the greatest common factor of fractions 322/674, 414/766.
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 322/674,414/766?
Given fractions are 322/674,414/766
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 322/674,414/766, numerators are 322,414
Denominators are 674,766
The GCF of 322,414 is 46 .
LCM of 674,766 is 258142.
The greatest common factor of 322/674,414/766 = [GCF of 322,414]/[LCM of 674,766]= 46/258142
Therefore, the GCF of 322/674,414/766 is 46/258142.
To find the highest common factor of 322,414, we have to find the factors of both numbers and list the highest common factor.
The factors of 322 are 1, 2, 7, 14, 23, 46, 161, 322
The factors of 414 are 1, 2, 3, 6, 9, 18, 23, 46, 69, 138, 207, 414
The HCF of 322,414 is 46.
Lets's calculate GCF of 322,414
| 2 | 322, 414 |
| 23 | 161, 207 |
| 7, 9 |
∴ So the GCF of the given numbers is 2 x 23 = 46
Greatest Common Factor of 322,414 By Matching Biggest Common Factor Method
Now, list down the factors of 322
:1,2,7,14,23,46,161,322
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 322,414 . The biggest common factor number is the GCF number.
So the greatest common factor 322,414 is 46.
Lets's calculate LCM of 674,766
| 2 | 674, 766 |
| 337, 383 |
∴ So the LCM of the given numbers is 2 x 337 x 383 = 258142
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 46/258142
Therefore, the GCF of Fractions 322/674,414/766 is 46/258142
Least Common Multiple of 674,766 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 674,766 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(674,766) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(674,766) x common factors =2 x 1 = 2
LCM(674,766) = ( 674 × 766 ) / 2
LCM(674,766) = 516284 / 2
LCM(674,766) = 258142
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FAQs on GCF of Fractions of 322/674, 414/766
1. What is the HCF of 322,414?
The HCF of 322,414 is 46
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 322/674, 414/766?
Answer: GCF of Numerators as per given numbers 322/674, 414/766 is
GCF of Numerators i.e. for 322,414 is 46
LCM of denominators i.e. for 674,766 is 258142.
Thus, GCF of Fractions is 46/258142.Finally, GCF of Fractions for 322/674, 414/766 is 46/258142.