GCF of 43/49, 174/42, 418/415
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 43/49, 174/42, 418/415 i.e 1/122010 easily. The following is the detailed procedure to determine the greatest common factor of fractions 43/49, 174/42, 418/415.
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 43/49,174/42,418/415?
Given fractions are 43/49,174/42,418/415
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 43/49,174/42,418/415, numerators are 43,174,418
Denominators are 49,42,415
The GCF of 43,174,418 is 1 .
LCM of 49,42,415 is 122010.
The greatest common factor of 43/49,174/42,418/415 = [GCF of 43,174,418]/[LCM of 49,42,415]= 1/122010
Therefore, the GCF of 43/49,174/42,418/415 is 1/122010.
To find the highest common factor of 43,174,418, 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 174 are 1, 2, 3, 6, 29, 58, 87, 174
The factors of 418 are 1, 2, 11, 19, 22, 38, 209, 418
The HCF of 43,174,418 is 1.
Lets's calculate GCF of 43,174,418
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 43,174,418 By Matching Biggest Common Factor Method
Now, list down the factors of 43
:1,43
Now, list down the factors of 174
:1,2,3,6,29,58,87,174
Now, list down the factors of 418
:1,2,11,19,22,38,209,418
Greatest Common Factor
We found the factors 43,174,418 . The biggest common factor number is the GCF number.
So the greatest common factor 43,174,418 is 1.
Lets's calculate LCM of 49,42,415
| 7 | 49, 42, 415 |
| 7, 6, 415 |
∴ So the LCM of the given numbers is 7 x 7 x 6 x 415 = 122010
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/122010
Therefore, the GCF of Fractions 43/49,174/42,418/415 is 1/122010
Least Common Multiple of 49,42,415 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 49,42,415 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(49,42,415) = 1
common factors(in case of two or more numbers have common factors) = 7
GCF(49,42,415) x common factors =1 x 7 = 7
LCM(49,42,415) = ( 49 × 42 × 415 ) / 7
LCM(49,42,415) = 854070 / 7
LCM(49,42,415) = 122010
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FAQs on GCF of Fractions of 43/49, 174/42, 418/415
1. What is the HCF of 43,174,418?
The HCF of 43,174,418 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 43/49, 174/42, 418/415?
Answer: GCF of Numerators as per given numbers 43/49, 174/42, 418/415 is
GCF of Numerators i.e. for 43,174,418 is 1
LCM of denominators i.e. for 49,42,415 is 122010.
Thus, GCF of Fractions is 1/122010.Finally, GCF of Fractions for 43/49, 174/42, 418/415 is 1/122010.