GCF of 414/578, 582/740
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 414/578, 582/740 i.e 6/213860 easily. The following is the detailed procedure to determine the greatest common factor of fractions 414/578, 582/740.
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 414/578,582/740?
Given fractions are 414/578,582/740
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 414/578,582/740, numerators are 414,582
Denominators are 578,740
The GCF of 414,582 is 6 .
LCM of 578,740 is 213860.
The greatest common factor of 414/578,582/740 = [GCF of 414,582]/[LCM of 578,740]= 6/213860
Therefore, the GCF of 414/578,582/740 is 6/213860.
To find the highest common factor of 414,582, we have to find the factors of both numbers and list the highest common factor.
The factors of 414 are 1, 2, 3, 6, 9, 18, 23, 46, 69, 138, 207, 414
The factors of 582 are 1, 2, 3, 6, 97, 194, 291, 582
The HCF of 414,582 is 6.
Lets's calculate GCF of 414,582
| 2 | 414, 582 |
| 3 | 207, 291 |
| 69, 97 |
∴ So the GCF of the given numbers is 2 x 3 = 6
Greatest Common Factor of 414,582 By Matching Biggest Common Factor Method
Now, list down the factors of 414
:1,2,3,6,9,18,23,46,69,138,207,414
Now, list down the factors of 582
:1,2,3,6,97,194,291,582
Greatest Common Factor
We found the factors 414,582 . The biggest common factor number is the GCF number.
So the greatest common factor 414,582 is 6.
Lets's calculate LCM of 578,740
| 2 | 578, 740 |
| 289, 370 |
∴ So the LCM of the given numbers is 2 x 289 x 370 = 213860
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/213860
Therefore, the GCF of Fractions 414/578,582/740 is 6/213860
Least Common Multiple of 578,740 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 578,740 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(578,740) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(578,740) x common factors =2 x 1 = 2
LCM(578,740) = ( 578 × 740 ) / 2
LCM(578,740) = 427720 / 2
LCM(578,740) = 213860
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FAQs on GCF of Fractions of 414/578, 582/740
1. What is the HCF of 414,582?
The HCF of 414,582 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 414/578, 582/740?
Answer: GCF of Numerators as per given numbers 414/578, 582/740 is
GCF of Numerators i.e. for 414,582 is 6
LCM of denominators i.e. for 578,740 is 213860.
Thus, GCF of Fractions is 6/213860.Finally, GCF of Fractions for 414/578, 582/740 is 6/213860.