Use our free GCF of Fractions Calculator tool to compute the GCF of 616/400, 693/455 i.e 77/36400 easily. The following is the detailed procedure to determine the greatest common factor of fractions 616/400, 693/455.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 616/400,693/455
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 616/400,693/455, numerators are 616,693
Denominators are 400,455
The GCF of 616,693 is 77 .
LCM of 400,455 is 36400.
The greatest common factor of 616/400,693/455 = [GCF of 616,693]/[LCM of 400,455]= 77/36400
Therefore, the GCF of 616/400,693/455 is 77/36400.
To find the highest common factor of 616,693, we have to find the factors of both numbers and list the highest common factor.
The factors of 616 are 1, 2, 4, 7, 8, 11, 14, 22, 28, 44, 56, 77, 88, 154, 308, 616
The factors of 693 are 1, 3, 7, 9, 11, 21, 33, 63, 77, 99, 231, 693
The HCF of 616,693 is 77.
Lets's calculate GCF of 616,693
7 | 616, 693 |
11 | 88, 99 |
8, 9 |
∴ So the GCF of the given numbers is 7 x 11 = 77
Now, list down the factors of 616
:1,2,4,7,8,11,14,22,28,44,56,77,88,154,308,616
Now, list down the factors of 693
:1,3,7,9,11,21,33,63,77,99,231,693
Greatest Common Factor
We found the factors 616,693 . The biggest common factor number is the GCF number.
So the greatest common factor 616,693 is 77.
Lets's calculate LCM of 400,455
5 | 400, 455 |
80, 91 |
∴ So the LCM of the given numbers is 5 x 80 x 91 = 36400
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 77/36400
Therefore, the GCF of Fractions 616/400,693/455 is 77/36400
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 400,455 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(400,455) = 5
common factors(in case of two or more numbers have common factors) = 1
GCF(400,455) x common factors =5 x 1 = 5
LCM(400,455) = ( 400 × 455 ) / 5
LCM(400,455) = 182000 / 5
LCM(400,455) = 36400
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 616,693?
The HCF of 616,693 is 77
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 616/400, 693/455?
Answer: GCF of Numerators as per given numbers 616/400, 693/455 is
GCF of Numerators i.e. for 616,693 is 77
LCM of denominators i.e. for 400,455 is 36400.
Thus, GCF of Fractions is 77/36400.Finally, GCF of Fractions for 616/400, 693/455 is 77/36400.