Use our free GCF of Fractions Calculator tool to compute the GCF of 153/413, 969/846 i.e 51/349398 easily. The following is the detailed procedure to determine the greatest common factor of fractions 153/413, 969/846.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 153/413,969/846
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 153/413,969/846, numerators are 153,969
Denominators are 413,846
The GCF of 153,969 is 51 .
LCM of 413,846 is 349398.
The greatest common factor of 153/413,969/846 = [GCF of 153,969]/[LCM of 413,846]= 51/349398
Therefore, the GCF of 153/413,969/846 is 51/349398.
To find the highest common factor of 153,969, we have to find the factors of both numbers and list the highest common factor.
The factors of 153 are 1, 3, 9, 17, 51, 153
The factors of 969 are 1, 3, 17, 19, 51, 57, 323, 969
The HCF of 153,969 is 51.
Lets's calculate GCF of 153,969
3 | 153, 969 |
17 | 51, 323 |
3, 19 |
∴ So the GCF of the given numbers is 3 x 17 = 51
Now, list down the factors of 153
:1,3,9,17,51,153
Now, list down the factors of 969
:1,3,17,19,51,57,323,969
Greatest Common Factor
We found the factors 153,969 . The biggest common factor number is the GCF number.
So the greatest common factor 153,969 is 51.
Lets's calculate LCM of 413,846
Given numbers has no common factors except 1. So, there LCM is their product i.e 349398
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 51/349398
Therefore, the GCF of Fractions 153/413,969/846 is 51/349398
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 413,846 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(413,846) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(413,846) x common factors =1 x 1 = 1
LCM(413,846) = ( 413 × 846 ) / 1
LCM(413,846) = 349398 / 1
LCM(413,846) = 349398
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 153,969?
The HCF of 153,969 is 51
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 153/413, 969/846?
Answer: GCF of Numerators as per given numbers 153/413, 969/846 is
GCF of Numerators i.e. for 153,969 is 51
LCM of denominators i.e. for 413,846 is 349398.
Thus, GCF of Fractions is 51/349398.Finally, GCF of Fractions for 153/413, 969/846 is 51/349398.