GCF of 892/122, 5742/136
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 892/122, 5742/136 i.e 2/8296 easily. The following is the detailed procedure to determine the greatest common factor of fractions 892/122, 5742/136.
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 892/122,5742/136?
Given fractions are 892/122,5742/136
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 892/122,5742/136, numerators are 892,5742
Denominators are 122,136
The GCF of 892,5742 is 2 .
LCM of 122,136 is 8296.
The greatest common factor of 892/122,5742/136 = [GCF of 892,5742]/[LCM of 122,136]= 2/8296
Therefore, the GCF of 892/122,5742/136 is 2/8296.
To find the highest common factor of 892,5742, we have to find the factors of both numbers and list the highest common factor.
The factors of 892 are 1, 2, 4, 223, 446, 892
The factors of 5742 are 1, 2, 3, 6, 9, 11, 18, 22, 29, 33, 58, 66, 87, 99, 174, 198, 261, 319, 522, 638, 957, 1914, 2871, 5742
The HCF of 892,5742 is 2.
Lets's calculate GCF of 892,5742
| 2 | 892, 5742 |
| 446, 2871 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 892,5742 By Matching Biggest Common Factor Method
Now, list down the factors of 892
:1,2,4,223,446,892
Now, list down the factors of 5742
:1,2,3,6,9,11,18,22,29,33,58,66,87,99,174,198,261,319,522,638,957,1914,2871,5742
Greatest Common Factor
We found the factors 892,5742 . The biggest common factor number is the GCF number.
So the greatest common factor 892,5742 is 2.
Lets's calculate LCM of 122,136
| 2 | 122, 136 |
| 61, 68 |
∴ So the LCM of the given numbers is 2 x 61 x 68 = 8296
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/8296
Therefore, the GCF of Fractions 892/122,5742/136 is 2/8296
Least Common Multiple of 122,136 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 122,136 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(122,136) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(122,136) x common factors =2 x 1 = 2
LCM(122,136) = ( 122 × 136 ) / 2
LCM(122,136) = 16592 / 2
LCM(122,136) = 8296
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FAQs on GCF of Fractions of 892/122, 5742/136
1. What is the HCF of 892,5742?
The HCF of 892,5742 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 892/122, 5742/136?
Answer: GCF of Numerators as per given numbers 892/122, 5742/136 is
GCF of Numerators i.e. for 892,5742 is 2
LCM of denominators i.e. for 122,136 is 8296.
Thus, GCF of Fractions is 2/8296.Finally, GCF of Fractions for 892/122, 5742/136 is 2/8296.