GCF of 610/49, 742/1457
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 610/49, 742/1457 i.e 2/71393 easily. The following is the detailed procedure to determine the greatest common factor of fractions 610/49, 742/1457.
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 610/49,742/1457?
Given fractions are 610/49,742/1457
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 610/49,742/1457, numerators are 610,742
Denominators are 49,1457
The GCF of 610,742 is 2 .
LCM of 49,1457 is 71393.
The greatest common factor of 610/49,742/1457 = [GCF of 610,742]/[LCM of 49,1457]= 2/71393
Therefore, the GCF of 610/49,742/1457 is 2/71393.
To find the highest common factor of 610,742, we have to find the factors of both numbers and list the highest common factor.
The factors of 610 are 1, 2, 5, 10, 61, 122, 305, 610
The factors of 742 are 1, 2, 7, 14, 53, 106, 371, 742
The HCF of 610,742 is 2.
Lets's calculate GCF of 610,742
| 2 | 610, 742 |
| 305, 371 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 610,742 By Matching Biggest Common Factor Method
Now, list down the factors of 610
:1,2,5,10,61,122,305,610
Now, list down the factors of 742
:1,2,7,14,53,106,371,742
Greatest Common Factor
We found the factors 610,742 . The biggest common factor number is the GCF number.
So the greatest common factor 610,742 is 2.
Lets's calculate LCM of 49,1457
Given numbers has no common factors except 1. So, there LCM is their product i.e 71393
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/71393
Therefore, the GCF of Fractions 610/49,742/1457 is 2/71393
Least Common Multiple of 49,1457 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 49,1457 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(49,1457) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(49,1457) x common factors =1 x 1 = 1
LCM(49,1457) = ( 49 × 1457 ) / 1
LCM(49,1457) = 71393 / 1
LCM(49,1457) = 71393
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FAQs on GCF of Fractions of 610/49, 742/1457
1. What is the HCF of 610,742?
The HCF of 610,742 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 610/49, 742/1457?
Answer: GCF of Numerators as per given numbers 610/49, 742/1457 is
GCF of Numerators i.e. for 610,742 is 2
LCM of denominators i.e. for 49,1457 is 71393.
Thus, GCF of Fractions is 2/71393.Finally, GCF of Fractions for 610/49, 742/1457 is 2/71393.