Use our free GCF of Fractions Calculator tool to compute the GCF of 987/413, 924/357 i.e 21/21063 easily. The following is the detailed procedure to determine the greatest common factor of fractions 987/413, 924/357.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 987/413,924/357
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 987/413,924/357, numerators are 987,924
Denominators are 413,357
The GCF of 987,924 is 21 .
LCM of 413,357 is 21063.
The greatest common factor of 987/413,924/357 = [GCF of 987,924]/[LCM of 413,357]= 21/21063
Therefore, the GCF of 987/413,924/357 is 21/21063.
To find the highest common factor of 987,924, we have to find the factors of both numbers and list the highest common factor.
The factors of 987 are 1, 3, 7, 21, 47, 141, 329, 987
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 987,924 is 21.
Lets's calculate GCF of 987,924
3 | 987, 924 |
7 | 329, 308 |
47, 44 |
∴ So the GCF of the given numbers is 3 x 7 = 21
Now, list down the factors of 987
:1,3,7,21,47,141,329,987
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 987,924 . The biggest common factor number is the GCF number.
So the greatest common factor 987,924 is 21.
Lets's calculate LCM of 413,357
7 | 413, 357 |
59, 51 |
∴ So the LCM of the given numbers is 7 x 59 x 51 = 21063
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 21/21063
Therefore, the GCF of Fractions 987/413,924/357 is 21/21063
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 413,357 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(413,357) = 7
common factors(in case of two or more numbers have common factors) = 1
GCF(413,357) x common factors =7 x 1 = 7
LCM(413,357) = ( 413 × 357 ) / 7
LCM(413,357) = 147441 / 7
LCM(413,357) = 21063
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 987,924?
The HCF of 987,924 is 21
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 987/413, 924/357?
Answer: GCF of Numerators as per given numbers 987/413, 924/357 is
GCF of Numerators i.e. for 987,924 is 21
LCM of denominators i.e. for 413,357 is 21063.
Thus, GCF of Fractions is 21/21063.Finally, GCF of Fractions for 987/413, 924/357 is 21/21063.