Use our free GCF of Fractions Calculator tool to compute the GCF of 735/614, 674/416 i.e 1/127712 easily. The following is the detailed procedure to determine the greatest common factor of fractions 735/614, 674/416.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 735/614,674/416
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 735/614,674/416, numerators are 735,674
Denominators are 614,416
The GCF of 735,674 is 1 .
LCM of 614,416 is 127712.
The greatest common factor of 735/614,674/416 = [GCF of 735,674]/[LCM of 614,416]= 1/127712
Therefore, the GCF of 735/614,674/416 is 1/127712.
To find the highest common factor of 735,674, we have to find the factors of both numbers and list the highest common factor.
The factors of 735 are 1, 3, 5, 7, 15, 21, 35, 49, 105, 147, 245, 735
The factors of 674 are 1, 2, 337, 674
The HCF of 735,674 is 1.
Lets's calculate GCF of 735,674
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 735
:1,3,5,7,15,21,35,49,105,147,245,735
Now, list down the factors of 674
:1,2,337,674
Greatest Common Factor
We found the factors 735,674 . The biggest common factor number is the GCF number.
So the greatest common factor 735,674 is 1.
Lets's calculate LCM of 614,416
2 | 614, 416 |
307, 208 |
∴ So the LCM of the given numbers is 2 x 307 x 208 = 127712
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/127712
Therefore, the GCF of Fractions 735/614,674/416 is 1/127712
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 614,416 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(614,416) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(614,416) x common factors =2 x 1 = 2
LCM(614,416) = ( 614 × 416 ) / 2
LCM(614,416) = 255424 / 2
LCM(614,416) = 127712
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 735,674?
The HCF of 735,674 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 735/614, 674/416?
Answer: GCF of Numerators as per given numbers 735/614, 674/416 is
GCF of Numerators i.e. for 735,674 is 1
LCM of denominators i.e. for 614,416 is 127712.
Thus, GCF of Fractions is 1/127712.Finally, GCF of Fractions for 735/614, 674/416 is 1/127712.