GCF of 4298/462, 8174/2724
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 4298/462, 8174/2724 i.e 2/209748 easily. The following is the detailed procedure to determine the greatest common factor of fractions 4298/462, 8174/2724.
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 4298/462,8174/2724?
Given fractions are 4298/462,8174/2724
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 4298/462,8174/2724, numerators are 4298,8174
Denominators are 462,2724
The GCF of 4298,8174 is 2 .
LCM of 462,2724 is 209748.
The greatest common factor of 4298/462,8174/2724 = [GCF of 4298,8174]/[LCM of 462,2724]= 2/209748
Therefore, the GCF of 4298/462,8174/2724 is 2/209748.
To find the highest common factor of 4298,8174, we have to find the factors of both numbers and list the highest common factor.
The factors of 4298 are 1, 2, 7, 14, 307, 614, 2149, 4298
The factors of 8174 are 1, 2, 61, 67, 122, 134, 4087, 8174
The HCF of 4298,8174 is 2.
Lets's calculate GCF of 4298,8174
| 2 | 4298, 8174 |
| 2149, 4087 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 4298,8174 By Matching Biggest Common Factor Method
Now, list down the factors of 4298
:1,2,7,14,307,614,2149,4298
Now, list down the factors of 8174
:1,2,61,67,122,134,4087,8174
Greatest Common Factor
We found the factors 4298,8174 . The biggest common factor number is the GCF number.
So the greatest common factor 4298,8174 is 2.
Lets's calculate LCM of 462,2724
| 2 | 462, 2724 |
| 3 | 231, 1362 |
| 77, 454 |
∴ So the LCM of the given numbers is 2 x 3 x 77 x 454 = 209748
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/209748
Therefore, the GCF of Fractions 4298/462,8174/2724 is 2/209748
Least Common Multiple of 462,2724 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 462,2724 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(462,2724) = 6
common factors(in case of two or more numbers have common factors) = 1
GCF(462,2724) x common factors =6 x 1 = 6
LCM(462,2724) = ( 462 × 2724 ) / 6
LCM(462,2724) = 1258488 / 6
LCM(462,2724) = 209748
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FAQs on GCF of Fractions of 4298/462, 8174/2724
1. What is the HCF of 4298,8174?
The HCF of 4298,8174 is 2
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 4298/462, 8174/2724?
Answer: GCF of Numerators as per given numbers 4298/462, 8174/2724 is
GCF of Numerators i.e. for 4298,8174 is 2
LCM of denominators i.e. for 462,2724 is 209748.
Thus, GCF of Fractions is 2/209748.Finally, GCF of Fractions for 4298/462, 8174/2724 is 2/209748.