GCF of 722/135, 830/171
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 722/135, 830/171 i.e 2/2565 easily. The following is the detailed procedure to determine the greatest common factor of fractions 722/135, 830/171.
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 722/135,830/171?
Given fractions are 722/135,830/171
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 722/135,830/171, numerators are 722,830
Denominators are 135,171
The GCF of 722,830 is 2 .
LCM of 135,171 is 2565.
The greatest common factor of 722/135,830/171 = [GCF of 722,830]/[LCM of 135,171]= 2/2565
Therefore, the GCF of 722/135,830/171 is 2/2565.
To find the highest common factor of 722,830, we have to find the factors of both numbers and list the highest common factor.
The factors of 722 are 1, 2, 19, 38, 361, 722
The factors of 830 are 1, 2, 5, 10, 83, 166, 415, 830
The HCF of 722,830 is 2.
Lets's calculate GCF of 722,830
| 2 | 722, 830 |
| 361, 415 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 722,830 By Matching Biggest Common Factor Method
Now, list down the factors of 722
:1,2,19,38,361,722
Now, list down the factors of 830
:1,2,5,10,83,166,415,830
Greatest Common Factor
We found the factors 722,830 . The biggest common factor number is the GCF number.
So the greatest common factor 722,830 is 2.
Lets's calculate LCM of 135,171
| 3 | 135, 171 |
| 3 | 45, 57 |
| 15, 19 |
∴ So the LCM of the given numbers is 3 x 3 x 15 x 19 = 2565
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/2565
Therefore, the GCF of Fractions 722/135,830/171 is 2/2565
Least Common Multiple of 135,171 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 135,171 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(135,171) = 9
common factors(in case of two or more numbers have common factors) = 1
GCF(135,171) x common factors =9 x 1 = 9
LCM(135,171) = ( 135 × 171 ) / 9
LCM(135,171) = 23085 / 9
LCM(135,171) = 2565
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FAQs on GCF of Fractions of 722/135, 830/171
1. What is the HCF of 722,830?
The HCF of 722,830 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 722/135, 830/171?
Answer: GCF of Numerators as per given numbers 722/135, 830/171 is
GCF of Numerators i.e. for 722,830 is 2
LCM of denominators i.e. for 135,171 is 2565.
Thus, GCF of Fractions is 2/2565.Finally, GCF of Fractions for 722/135, 830/171 is 2/2565.