GCF of 153/40, 306/674
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 153/40, 306/674 i.e 153/13480 easily. The following is the detailed procedure to determine the greatest common factor of fractions 153/40, 306/674.
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 153/40,306/674?
Given fractions are 153/40,306/674
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 153/40,306/674, numerators are 153,306
Denominators are 40,674
The GCF of 153,306 is 153 .
LCM of 40,674 is 13480.
The greatest common factor of 153/40,306/674 = [GCF of 153,306]/[LCM of 40,674]= 153/13480
Therefore, the GCF of 153/40,306/674 is 153/13480.
To find the highest common factor of 153,306, 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 306 are 1, 2, 3, 6, 9, 17, 18, 34, 51, 102, 153, 306
The HCF of 153,306 is 153.
Lets's calculate GCF of 153,306
| 3 | 153, 306 |
| 3 | 51, 102 |
| 17 | 17, 34 |
| 1, 2 |
∴ So the GCF of the given numbers is 3 x 3 x 17 = 153
Greatest Common Factor of 153,306 By Matching Biggest Common Factor Method
Now, list down the factors of 153
:1,3,9,17,51,153
Now, list down the factors of 306
:1,2,3,6,9,17,18,34,51,102,153,306
Greatest Common Factor
We found the factors 153,306 . The biggest common factor number is the GCF number.
So the greatest common factor 153,306 is 153.
Lets's calculate LCM of 40,674
| 2 | 40, 674 |
| 20, 337 |
∴ So the LCM of the given numbers is 2 x 20 x 337 = 13480
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 153/13480
Therefore, the GCF of Fractions 153/40,306/674 is 153/13480
Least Common Multiple of 40,674 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 40,674 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(40,674) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(40,674) x common factors =2 x 1 = 2
LCM(40,674) = ( 40 × 674 ) / 2
LCM(40,674) = 26960 / 2
LCM(40,674) = 13480
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FAQs on GCF of Fractions of 153/40, 306/674
1. What is the HCF of 153,306?
The HCF of 153,306 is 153
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 153/40, 306/674?
Answer: GCF of Numerators as per given numbers 153/40, 306/674 is
GCF of Numerators i.e. for 153,306 is 153
LCM of denominators i.e. for 40,674 is 13480.
Thus, GCF of Fractions is 153/13480.Finally, GCF of Fractions for 153/40, 306/674 is 153/13480.