Use our free GCF of Fractions Calculator tool to compute the GCF of 296/749, 616/861 i.e 8/92127 easily. The following is the detailed procedure to determine the greatest common factor of fractions 296/749, 616/861.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 296/749,616/861
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 296/749,616/861, numerators are 296,616
Denominators are 749,861
The GCF of 296,616 is 8 .
LCM of 749,861 is 92127.
The greatest common factor of 296/749,616/861 = [GCF of 296,616]/[LCM of 749,861]= 8/92127
Therefore, the GCF of 296/749,616/861 is 8/92127.
To find the highest common factor of 296,616, we have to find the factors of both numbers and list the highest common factor.
The factors of 296 are 1, 2, 4, 8, 37, 74, 148, 296
The factors of 616 are 1, 2, 4, 7, 8, 11, 14, 22, 28, 44, 56, 77, 88, 154, 308, 616
The HCF of 296,616 is 8.
Lets's calculate GCF of 296,616
2 | 296, 616 |
2 | 148, 308 |
2 | 74, 154 |
37, 77 |
∴ So the GCF of the given numbers is 2 x 2 x 2 = 8
Now, list down the factors of 296
:1,2,4,8,37,74,148,296
Now, list down the factors of 616
:1,2,4,7,8,11,14,22,28,44,56,77,88,154,308,616
Greatest Common Factor
We found the factors 296,616 . The biggest common factor number is the GCF number.
So the greatest common factor 296,616 is 8.
Lets's calculate LCM of 749,861
7 | 749, 861 |
107, 123 |
∴ So the LCM of the given numbers is 7 x 107 x 123 = 92127
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 8/92127
Therefore, the GCF of Fractions 296/749,616/861 is 8/92127
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 749,861 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(749,861) = 7
common factors(in case of two or more numbers have common factors) = 1
GCF(749,861) x common factors =7 x 1 = 7
LCM(749,861) = ( 749 × 861 ) / 7
LCM(749,861) = 644889 / 7
LCM(749,861) = 92127
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 296,616?
The HCF of 296,616 is 8
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 296/749, 616/861?
Answer: GCF of Numerators as per given numbers 296/749, 616/861 is
GCF of Numerators i.e. for 296,616 is 8
LCM of denominators i.e. for 749,861 is 92127.
Thus, GCF of Fractions is 8/92127.Finally, GCF of Fractions for 296/749, 616/861 is 8/92127.