Use our free GCF of Fractions Calculator tool to compute the GCF of 416/839, 762/102 i.e 2/85578 easily. The following is the detailed procedure to determine the greatest common factor of fractions 416/839, 762/102.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 416/839,762/102
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 416/839,762/102, numerators are 416,762
Denominators are 839,102
The GCF of 416,762 is 2 .
LCM of 839,102 is 85578.
The greatest common factor of 416/839,762/102 = [GCF of 416,762]/[LCM of 839,102]= 2/85578
Therefore, the GCF of 416/839,762/102 is 2/85578.
To find the highest common factor of 416,762, we have to find the factors of both numbers and list the highest common factor.
The factors of 416 are 1, 2, 4, 8, 13, 16, 26, 32, 52, 104, 208, 416
The factors of 762 are 1, 2, 3, 6, 127, 254, 381, 762
The HCF of 416,762 is 2.
Lets's calculate GCF of 416,762
2 | 416, 762 |
208, 381 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 416
:1,2,4,8,13,16,26,32,52,104,208,416
Now, list down the factors of 762
:1,2,3,6,127,254,381,762
Greatest Common Factor
We found the factors 416,762 . The biggest common factor number is the GCF number.
So the greatest common factor 416,762 is 2.
Lets's calculate LCM of 839,102
Given numbers has no common factors except 1. So, there LCM is their product i.e 85578
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/85578
Therefore, the GCF of Fractions 416/839,762/102 is 2/85578
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 839,102 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(839,102) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(839,102) x common factors =1 x 1 = 1
LCM(839,102) = ( 839 × 102 ) / 1
LCM(839,102) = 85578 / 1
LCM(839,102) = 85578
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 416,762?
The HCF of 416,762 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 416/839, 762/102?
Answer: GCF of Numerators as per given numbers 416/839, 762/102 is
GCF of Numerators i.e. for 416,762 is 2
LCM of denominators i.e. for 839,102 is 85578.
Thus, GCF of Fractions is 2/85578.Finally, GCF of Fractions for 416/839, 762/102 is 2/85578.