GCF of 43/29, 42/541, 749/289
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 43/29, 42/541, 749/289 i.e 1/4534121 easily. The following is the detailed procedure to determine the greatest common factor of fractions 43/29, 42/541, 749/289.
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 43/29,42/541,749/289?
Given fractions are 43/29,42/541,749/289
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 43/29,42/541,749/289, numerators are 43,42,749
Denominators are 29,541,289
The GCF of 43,42,749 is 1 .
LCM of 29,541,289 is 4534121.
The greatest common factor of 43/29,42/541,749/289 = [GCF of 43,42,749]/[LCM of 29,541,289]= 1/4534121
Therefore, the GCF of 43/29,42/541,749/289 is 1/4534121.
To find the highest common factor of 43,42,749, we have to find the factors of both numbers and list the highest common factor.
The factors of 43 are 1, 43
The factors of 42 are 1, 2, 3, 6, 7, 14, 21, 42
The factors of 749 are 1, 7, 107, 749
The HCF of 43,42,749 is 1.
Lets's calculate GCF of 43,42,749
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 43,42,749 By Matching Biggest Common Factor Method
Now, list down the factors of 43
:1,43
Now, list down the factors of 42
:1,2,3,6,7,14,21,42
Now, list down the factors of 749
:1,7,107,749
Greatest Common Factor
We found the factors 43,42,749 . The biggest common factor number is the GCF number.
So the greatest common factor 43,42,749 is 1.
Lets's calculate LCM of 29,541,289
Given numbers has no common factors except 1. So, there LCM is their product i.e 4534121
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/4534121
Therefore, the GCF of Fractions 43/29,42/541,749/289 is 1/4534121
Least Common Multiple of 29,541,289 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 29,541,289 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(29,541,289) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(29,541,289) x common factors =1 x 1 = 1
LCM(29,541,289) = ( 29 × 541 × 289 ) / 1
LCM(29,541,289) = 4534121 / 1
LCM(29,541,289) = 4534121
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FAQs on GCF of Fractions of 43/29, 42/541, 749/289
1. What is the HCF of 43,42,749?
The HCF of 43,42,749 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 43/29, 42/541, 749/289?
Answer: GCF of Numerators as per given numbers 43/29, 42/541, 749/289 is
GCF of Numerators i.e. for 43,42,749 is 1
LCM of denominators i.e. for 29,541,289 is 4534121.
Thus, GCF of Fractions is 1/4534121.Finally, GCF of Fractions for 43/29, 42/541, 749/289 is 1/4534121.