GCF of 161/820, 138/830
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 161/820, 138/830 i.e 23/68060 easily. The following is the detailed procedure to determine the greatest common factor of fractions 161/820, 138/830.
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 161/820,138/830?
Given fractions are 161/820,138/830
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 161/820,138/830, numerators are 161,138
Denominators are 820,830
The GCF of 161,138 is 23 .
LCM of 820,830 is 68060.
The greatest common factor of 161/820,138/830 = [GCF of 161,138]/[LCM of 820,830]= 23/68060
Therefore, the GCF of 161/820,138/830 is 23/68060.
To find the highest common factor of 161,138, we have to find the factors of both numbers and list the highest common factor.
The factors of 161 are 1, 7, 23, 161
The factors of 138 are 1, 2, 3, 6, 23, 46, 69, 138
The HCF of 161,138 is 23.
Lets's calculate GCF of 161,138
| 23 | 161, 138 |
| 7, 6 |
∴ So the GCF of the given numbers is 23 = 23
Greatest Common Factor of 161,138 By Matching Biggest Common Factor Method
Now, list down the factors of 161
:1,7,23,161
Now, list down the factors of 138
:1,2,3,6,23,46,69,138
Greatest Common Factor
We found the factors 161,138 . The biggest common factor number is the GCF number.
So the greatest common factor 161,138 is 23.
Lets's calculate LCM of 820,830
| 2 | 820, 830 |
| 5 | 410, 415 |
| 82, 83 |
∴ So the LCM of the given numbers is 2 x 5 x 82 x 83 = 68060
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 23/68060
Therefore, the GCF of Fractions 161/820,138/830 is 23/68060
Least Common Multiple of 820,830 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 820,830 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(820,830) = 10
common factors(in case of two or more numbers have common factors) = 1
GCF(820,830) x common factors =10 x 1 = 10
LCM(820,830) = ( 820 × 830 ) / 10
LCM(820,830) = 680600 / 10
LCM(820,830) = 68060
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FAQs on GCF of Fractions of 161/820, 138/830
1. What is the HCF of 161,138?
The HCF of 161,138 is 23
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 161/820, 138/830?
Answer: GCF of Numerators as per given numbers 161/820, 138/830 is
GCF of Numerators i.e. for 161,138 is 23
LCM of denominators i.e. for 820,830 is 68060.
Thus, GCF of Fractions is 23/68060.Finally, GCF of Fractions for 161/820, 138/830 is 23/68060.