Use our free GCF of Fractions Calculator tool to compute the GCF of 749/612, 924/864 i.e 7/14688 easily. The following is the detailed procedure to determine the greatest common factor of fractions 749/612, 924/864.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 749/612,924/864
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 749/612,924/864, numerators are 749,924
Denominators are 612,864
The GCF of 749,924 is 7 .
LCM of 612,864 is 14688.
The greatest common factor of 749/612,924/864 = [GCF of 749,924]/[LCM of 612,864]= 7/14688
Therefore, the GCF of 749/612,924/864 is 7/14688.
To find the highest common factor of 749,924, we have to find the factors of both numbers and list the highest common factor.
The factors of 749 are 1, 7, 107, 749
The factors of 924 are 1, 2, 3, 4, 6, 7, 11, 12, 14, 21, 22, 28, 33, 42, 44, 66, 77, 84, 132, 154, 231, 308, 462, 924
The HCF of 749,924 is 7.
Lets's calculate GCF of 749,924
7 | 749, 924 |
107, 132 |
∴ So the GCF of the given numbers is 7 = 7
Now, list down the factors of 749
:1,7,107,749
Now, list down the factors of 924
:1,2,3,4,6,7,11,12,14,21,22,28,33,42,44,66,77,84,132,154,231,308,462,924
Greatest Common Factor
We found the factors 749,924 . The biggest common factor number is the GCF number.
So the greatest common factor 749,924 is 7.
Lets's calculate LCM of 612,864
2 | 612, 864 |
2 | 306, 432 |
3 | 153, 216 |
3 | 51, 72 |
17, 24 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 3 x 17 x 24 = 14688
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 7/14688
Therefore, the GCF of Fractions 749/612,924/864 is 7/14688
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 612,864 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(612,864) = 36
common factors(in case of two or more numbers have common factors) = 1
GCF(612,864) x common factors =36 x 1 = 36
LCM(612,864) = ( 612 × 864 ) / 36
LCM(612,864) = 528768 / 36
LCM(612,864) = 14688
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 749,924?
The HCF of 749,924 is 7
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 749/612, 924/864?
Answer: GCF of Numerators as per given numbers 749/612, 924/864 is
GCF of Numerators i.e. for 749,924 is 7
LCM of denominators i.e. for 612,864 is 14688.
Thus, GCF of Fractions is 7/14688.Finally, GCF of Fractions for 749/612, 924/864 is 7/14688.