GCF of 149/40, 189/278
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 149/40, 189/278 i.e 1/5560 easily. The following is the detailed procedure to determine the greatest common factor of fractions 149/40, 189/278.
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 149/40,189/278?
Given fractions are 149/40,189/278
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 149/40,189/278, numerators are 149,189
Denominators are 40,278
The GCF of 149,189 is 1 .
LCM of 40,278 is 5560.
The greatest common factor of 149/40,189/278 = [GCF of 149,189]/[LCM of 40,278]= 1/5560
Therefore, the GCF of 149/40,189/278 is 1/5560.
To find the highest common factor of 149,189, we have to find the factors of both numbers and list the highest common factor.
The factors of 149 are 1, 149
The factors of 189 are 1, 3, 7, 9, 21, 27, 63, 189
The HCF of 149,189 is 1.
Lets's calculate GCF of 149,189
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 149,189 By Matching Biggest Common Factor Method
Now, list down the factors of 149
:1,149
Now, list down the factors of 189
:1,3,7,9,21,27,63,189
Greatest Common Factor
We found the factors 149,189 . The biggest common factor number is the GCF number.
So the greatest common factor 149,189 is 1.
Lets's calculate LCM of 40,278
| 2 | 40, 278 |
| 20, 139 |
∴ So the LCM of the given numbers is 2 x 20 x 139 = 5560
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/5560
Therefore, the GCF of Fractions 149/40,189/278 is 1/5560
Least Common Multiple of 40,278 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 40,278 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(40,278) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(40,278) x common factors =2 x 1 = 2
LCM(40,278) = ( 40 × 278 ) / 2
LCM(40,278) = 11120 / 2
LCM(40,278) = 5560
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FAQs on GCF of Fractions of 149/40, 189/278
1. What is the HCF of 149,189?
The HCF of 149,189 is 1
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 149/40, 189/278?
Answer: GCF of Numerators as per given numbers 149/40, 189/278 is
GCF of Numerators i.e. for 149,189 is 1
LCM of denominators i.e. for 40,278 is 5560.
Thus, GCF of Fractions is 1/5560.Finally, GCF of Fractions for 149/40, 189/278 is 1/5560.