Use our free GCF of Fractions Calculator tool to compute the GCF of 874/643, 969/128 i.e 19/82304 easily. The following is the detailed procedure to determine the greatest common factor of fractions 874/643, 969/128.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 874/643,969/128
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 874/643,969/128, numerators are 874,969
Denominators are 643,128
The GCF of 874,969 is 19 .
LCM of 643,128 is 82304.
The greatest common factor of 874/643,969/128 = [GCF of 874,969]/[LCM of 643,128]= 19/82304
Therefore, the GCF of 874/643,969/128 is 19/82304.
To find the highest common factor of 874,969, we have to find the factors of both numbers and list the highest common factor.
The factors of 874 are 1, 2, 19, 23, 38, 46, 437, 874
The factors of 969 are 1, 3, 17, 19, 51, 57, 323, 969
The HCF of 874,969 is 19.
Lets's calculate GCF of 874,969
19 | 874, 969 |
46, 51 |
∴ So the GCF of the given numbers is 19 = 19
Now, list down the factors of 874
:1,2,19,23,38,46,437,874
Now, list down the factors of 969
:1,3,17,19,51,57,323,969
Greatest Common Factor
We found the factors 874,969 . The biggest common factor number is the GCF number.
So the greatest common factor 874,969 is 19.
Lets's calculate LCM of 643,128
Given numbers has no common factors except 1. So, there LCM is their product i.e 82304
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 19/82304
Therefore, the GCF of Fractions 874/643,969/128 is 19/82304
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 643,128 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(643,128) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(643,128) x common factors =1 x 1 = 1
LCM(643,128) = ( 643 × 128 ) / 1
LCM(643,128) = 82304 / 1
LCM(643,128) = 82304
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 874,969?
The HCF of 874,969 is 19
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 874/643, 969/128?
Answer: GCF of Numerators as per given numbers 874/643, 969/128 is
GCF of Numerators i.e. for 874,969 is 19
LCM of denominators i.e. for 643,128 is 82304.
Thus, GCF of Fractions is 19/82304.Finally, GCF of Fractions for 874/643, 969/128 is 19/82304.