Use our free GCF of Fractions Calculator tool to compute the GCF of 1292/153, 1734/506 i.e 34/77418 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1292/153, 1734/506.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 1292/153,1734/506
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 1292/153,1734/506, numerators are 1292,1734
Denominators are 153,506
The GCF of 1292,1734 is 34 .
LCM of 153,506 is 77418.
The greatest common factor of 1292/153,1734/506 = [GCF of 1292,1734]/[LCM of 153,506]= 34/77418
Therefore, the GCF of 1292/153,1734/506 is 34/77418.
To find the highest common factor of 1292,1734, we have to find the factors of both numbers and list the highest common factor.
The factors of 1292 are 1, 2, 4, 17, 19, 34, 38, 68, 76, 323, 646, 1292
The factors of 1734 are 1, 2, 3, 6, 17, 34, 51, 102, 289, 578, 867, 1734
The HCF of 1292,1734 is 34.
Lets's calculate GCF of 1292,1734
2 | 1292, 1734 |
17 | 646, 867 |
38, 51 |
∴ So the GCF of the given numbers is 2 x 17 = 34
Now, list down the factors of 1292
:1,2,4,17,19,34,38,68,76,323,646,1292
Now, list down the factors of 1734
:1,2,3,6,17,34,51,102,289,578,867,1734
Greatest Common Factor
We found the factors 1292,1734 . The biggest common factor number is the GCF number.
So the greatest common factor 1292,1734 is 34.
Lets's calculate LCM of 153,506
Given numbers has no common factors except 1. So, there LCM is their product i.e 77418
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 34/77418
Therefore, the GCF of Fractions 1292/153,1734/506 is 34/77418
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 153,506 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(153,506) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(153,506) x common factors =1 x 1 = 1
LCM(153,506) = ( 153 × 506 ) / 1
LCM(153,506) = 77418 / 1
LCM(153,506) = 77418
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 1292,1734?
The HCF of 1292,1734 is 34
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 1292/153, 1734/506?
Answer: GCF of Numerators as per given numbers 1292/153, 1734/506 is
GCF of Numerators i.e. for 1292,1734 is 34
LCM of denominators i.e. for 153,506 is 77418.
Thus, GCF of Fractions is 34/77418.Finally, GCF of Fractions for 1292/153, 1734/506 is 34/77418.