GCF of 382/912, 3640/614
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 382/912, 3640/614 i.e 2/279984 easily. The following is the detailed procedure to determine the greatest common factor of fractions 382/912, 3640/614.
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 382/912,3640/614?
Given fractions are 382/912,3640/614
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 382/912,3640/614, numerators are 382,3640
Denominators are 912,614
The GCF of 382,3640 is 2 .
LCM of 912,614 is 279984.
The greatest common factor of 382/912,3640/614 = [GCF of 382,3640]/[LCM of 912,614]= 2/279984
Therefore, the GCF of 382/912,3640/614 is 2/279984.
To find the highest common factor of 382,3640, we have to find the factors of both numbers and list the highest common factor.
The factors of 382 are 1, 2, 191, 382
The factors of 3640 are 1, 2, 4, 5, 7, 8, 10, 13, 14, 20, 26, 28, 35, 40, 52, 56, 65, 70, 91, 104, 130, 140, 182, 260, 280, 364, 455, 520, 728, 910, 1820, 3640
The HCF of 382,3640 is 2.
Lets's calculate GCF of 382,3640
| 2 | 382, 3640 |
| 191, 1820 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 382,3640 By Matching Biggest Common Factor Method
Now, list down the factors of 382
:1,2,191,382
Now, list down the factors of 3640
:1,2,4,5,7,8,10,13,14,20,26,28,35,40,52,56,65,70,91,104,130,140,182,260,280,364,455,520,728,910,1820,3640
Greatest Common Factor
We found the factors 382,3640 . The biggest common factor number is the GCF number.
So the greatest common factor 382,3640 is 2.
Lets's calculate LCM of 912,614
| 2 | 912, 614 |
| 456, 307 |
∴ So the LCM of the given numbers is 2 x 456 x 307 = 279984
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/279984
Therefore, the GCF of Fractions 382/912,3640/614 is 2/279984
Least Common Multiple of 912,614 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 912,614 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(912,614) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(912,614) x common factors =2 x 1 = 2
LCM(912,614) = ( 912 × 614 ) / 2
LCM(912,614) = 559968 / 2
LCM(912,614) = 279984
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FAQs on GCF of Fractions of 382/912, 3640/614
1. What is the HCF of 382,3640?
The HCF of 382,3640 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 382/912, 3640/614?
Answer: GCF of Numerators as per given numbers 382/912, 3640/614 is
GCF of Numerators i.e. for 382,3640 is 2
LCM of denominators i.e. for 912,614 is 279984.
Thus, GCF of Fractions is 2/279984.Finally, GCF of Fractions for 382/912, 3640/614 is 2/279984.