GCF of 154/198, 609/130
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 154/198, 609/130 i.e 7/12870 easily. The following is the detailed procedure to determine the greatest common factor of fractions 154/198, 609/130.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
What is the GCF of 154/198,609/130?
Given fractions are 154/198,609/130
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 154/198,609/130, numerators are 154,609
Denominators are 198,130
The GCF of 154,609 is 7 .
LCM of 198,130 is 12870.
The greatest common factor of 154/198,609/130 = [GCF of 154,609]/[LCM of 198,130]= 7/12870
Therefore, the GCF of 154/198,609/130 is 7/12870.
To find the highest common factor of 154,609, we have to find the factors of both numbers and list the highest common factor.
The factors of 154 are 1, 2, 7, 11, 14, 22, 77, 154
The factors of 609 are 1, 3, 7, 21, 29, 87, 203, 609
The HCF of 154,609 is 7.
Lets's calculate GCF of 154,609
| 7 | 154, 609 |
| 22, 87 |
∴ So the GCF of the given numbers is 7 = 7
Greatest Common Factor of 154,609 By Matching Biggest Common Factor Method
Now, list down the factors of 154
:1,2,7,11,14,22,77,154
Now, list down the factors of 609
:1,3,7,21,29,87,203,609
Greatest Common Factor
We found the factors 154,609 . The biggest common factor number is the GCF number.
So the greatest common factor 154,609 is 7.
Lets's calculate LCM of 198,130
| 2 | 198, 130 |
| 99, 65 |
∴ So the LCM of the given numbers is 2 x 99 x 65 = 12870
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 7/12870
Therefore, the GCF of Fractions 154/198,609/130 is 7/12870
Least Common Multiple of 198,130 with GCF Formula
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 198,130 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(198,130) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(198,130) x common factors =2 x 1 = 2
LCM(198,130) = ( 198 × 130 ) / 2
LCM(198,130) = 25740 / 2
LCM(198,130) = 12870
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FAQs on GCF of Fractions of 154/198, 609/130
1. What is the HCF of 154,609?
The HCF of 154,609 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 154/198, 609/130?
Answer: GCF of Numerators as per given numbers 154/198, 609/130 is
GCF of Numerators i.e. for 154,609 is 7
LCM of denominators i.e. for 198,130 is 12870.
Thus, GCF of Fractions is 7/12870.Finally, GCF of Fractions for 154/198, 609/130 is 7/12870.