GCF of 34/278, 31/361, 165/844
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 34/278, 31/361, 165/844 i.e 1/42351076 easily. The following is the detailed procedure to determine the greatest common factor of fractions 34/278, 31/361, 165/844.
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 34/278,31/361,165/844?
Given fractions are 34/278,31/361,165/844
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 34/278,31/361,165/844, numerators are 34,31,165
Denominators are 278,361,844
The GCF of 34,31,165 is 1 .
LCM of 278,361,844 is 42351076.
The greatest common factor of 34/278,31/361,165/844 = [GCF of 34,31,165]/[LCM of 278,361,844]= 1/42351076
Therefore, the GCF of 34/278,31/361,165/844 is 1/42351076.
To find the highest common factor of 34,31,165, we have to find the factors of both numbers and list the highest common factor.
The factors of 34 are 1, 2, 17, 34
The factors of 31 are 1, 31
The factors of 165 are 1, 3, 5, 11, 15, 33, 55, 165
The HCF of 34,31,165 is 1.
Lets's calculate GCF of 34,31,165
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 34,31,165 By Matching Biggest Common Factor Method
Now, list down the factors of 34
:1,2,17,34
Now, list down the factors of 31
:1,31
Now, list down the factors of 165
:1,3,5,11,15,33,55,165
Greatest Common Factor
We found the factors 34,31,165 . The biggest common factor number is the GCF number.
So the greatest common factor 34,31,165 is 1.
Lets's calculate LCM of 278,361,844
| 2 | 278, 361, 844 |
| 139, 361, 422 |
∴ So the LCM of the given numbers is 2 x 139 x 361 x 422 = 42351076
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/42351076
Therefore, the GCF of Fractions 34/278,31/361,165/844 is 1/42351076
Least Common Multiple of 278,361,844 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 278,361,844 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(278,361,844) = 1
common factors(in case of two or more numbers have common factors) = 2
GCF(278,361,844) x common factors =1 x 2 = 2
LCM(278,361,844) = ( 278 × 361 × 844 ) / 2
LCM(278,361,844) = 84702152 / 2
LCM(278,361,844) = 42351076
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FAQs on GCF of Fractions of 34/278, 31/361, 165/844
1. What is the HCF of 34,31,165?
The HCF of 34,31,165 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 34/278, 31/361, 165/844?
Answer: GCF of Numerators as per given numbers 34/278, 31/361, 165/844 is
GCF of Numerators i.e. for 34,31,165 is 1
LCM of denominators i.e. for 278,361,844 is 42351076.
Thus, GCF of Fractions is 1/42351076.Finally, GCF of Fractions for 34/278, 31/361, 165/844 is 1/42351076.