Use our free GCF of Fractions Calculator tool to compute the GCF of 416/100, 676/307 i.e 52/30700 easily. The following is the detailed procedure to determine the greatest common factor of fractions 416/100, 676/307.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 416/100,676/307
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 416/100,676/307, numerators are 416,676
Denominators are 100,307
The GCF of 416,676 is 52 .
LCM of 100,307 is 30700.
The greatest common factor of 416/100,676/307 = [GCF of 416,676]/[LCM of 100,307]= 52/30700
Therefore, the GCF of 416/100,676/307 is 52/30700.
To find the highest common factor of 416,676, 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 676 are 1, 2, 4, 13, 26, 52, 169, 338, 676
The HCF of 416,676 is 52.
Lets's calculate GCF of 416,676
2 | 416, 676 |
2 | 208, 338 |
13 | 104, 169 |
8, 13 |
∴ So the GCF of the given numbers is 2 x 2 x 13 = 52
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 676
:1,2,4,13,26,52,169,338,676
Greatest Common Factor
We found the factors 416,676 . The biggest common factor number is the GCF number.
So the greatest common factor 416,676 is 52.
Lets's calculate LCM of 100,307
Given numbers has no common factors except 1. So, there LCM is their product i.e 30700
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 52/30700
Therefore, the GCF of Fractions 416/100,676/307 is 52/30700
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 100,307 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(100,307) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(100,307) x common factors =1 x 1 = 1
LCM(100,307) = ( 100 × 307 ) / 1
LCM(100,307) = 30700 / 1
LCM(100,307) = 30700
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 416,676?
The HCF of 416,676 is 52
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 416/100, 676/307?
Answer: GCF of Numerators as per given numbers 416/100, 676/307 is
GCF of Numerators i.e. for 416,676 is 52
LCM of denominators i.e. for 100,307 is 30700.
Thus, GCF of Fractions is 52/30700.Finally, GCF of Fractions for 416/100, 676/307 is 52/30700.