GCF of 306/784, 649/465
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 306/784, 649/465 i.e 1/364560 easily. The following is the detailed procedure to determine the greatest common factor of fractions 306/784, 649/465.
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 306/784,649/465?
Given fractions are 306/784,649/465
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 306/784,649/465, numerators are 306,649
Denominators are 784,465
The GCF of 306,649 is 1 .
LCM of 784,465 is 364560.
The greatest common factor of 306/784,649/465 = [GCF of 306,649]/[LCM of 784,465]= 1/364560
Therefore, the GCF of 306/784,649/465 is 1/364560.
To find the highest common factor of 306,649, we have to find the factors of both numbers and list the highest common factor.
The factors of 306 are 1, 2, 3, 6, 9, 17, 18, 34, 51, 102, 153, 306
The factors of 649 are 1, 11, 59, 649
The HCF of 306,649 is 1.
Lets's calculate GCF of 306,649
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 306,649 By Matching Biggest Common Factor Method
Now, list down the factors of 306
:1,2,3,6,9,17,18,34,51,102,153,306
Now, list down the factors of 649
:1,11,59,649
Greatest Common Factor
We found the factors 306,649 . The biggest common factor number is the GCF number.
So the greatest common factor 306,649 is 1.
Lets's calculate LCM of 784,465
Given numbers has no common factors except 1. So, there LCM is their product i.e 364560
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/364560
Therefore, the GCF of Fractions 306/784,649/465 is 1/364560
Least Common Multiple of 784,465 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 784,465 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(784,465) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(784,465) x common factors =1 x 1 = 1
LCM(784,465) = ( 784 × 465 ) / 1
LCM(784,465) = 364560 / 1
LCM(784,465) = 364560
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FAQs on GCF of Fractions of 306/784, 649/465
1. What is the HCF of 306,649?
The HCF of 306,649 is 1
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 306/784, 649/465?
Answer: GCF of Numerators as per given numbers 306/784, 649/465 is
GCF of Numerators i.e. for 306,649 is 1
LCM of denominators i.e. for 784,465 is 364560.
Thus, GCF of Fractions is 1/364560.Finally, GCF of Fractions for 306/784, 649/465 is 1/364560.