GCF of 670/81, 140/217
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 670/81, 140/217 i.e 10/17577 easily. The following is the detailed procedure to determine the greatest common factor of fractions 670/81, 140/217.
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 670/81,140/217?
Given fractions are 670/81,140/217
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 670/81,140/217, numerators are 670,140
Denominators are 81,217
The GCF of 670,140 is 10 .
LCM of 81,217 is 17577.
The greatest common factor of 670/81,140/217 = [GCF of 670,140]/[LCM of 81,217]= 10/17577
Therefore, the GCF of 670/81,140/217 is 10/17577.
To find the highest common factor of 670,140, we have to find the factors of both numbers and list the highest common factor.
The factors of 670 are 1, 2, 5, 10, 67, 134, 335, 670
The factors of 140 are 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70, 140
The HCF of 670,140 is 10.
Lets's calculate GCF of 670,140
| 2 | 670, 140 |
| 5 | 335, 70 |
| 67, 14 |
∴ So the GCF of the given numbers is 2 x 5 = 10
Greatest Common Factor of 670,140 By Matching Biggest Common Factor Method
Now, list down the factors of 670
:1,2,5,10,67,134,335,670
Now, list down the factors of 140
:1,2,4,5,7,10,14,20,28,35,70,140
Greatest Common Factor
We found the factors 670,140 . The biggest common factor number is the GCF number.
So the greatest common factor 670,140 is 10.
Lets's calculate LCM of 81,217
Given numbers has no common factors except 1. So, there LCM is their product i.e 17577
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 10/17577
Therefore, the GCF of Fractions 670/81,140/217 is 10/17577
Least Common Multiple of 81,217 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 81,217 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(81,217) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(81,217) x common factors =1 x 1 = 1
LCM(81,217) = ( 81 × 217 ) / 1
LCM(81,217) = 17577 / 1
LCM(81,217) = 17577
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FAQs on GCF of Fractions of 670/81, 140/217
1. What is the HCF of 670,140?
The HCF of 670,140 is 10
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 670/81, 140/217?
Answer: GCF of Numerators as per given numbers 670/81, 140/217 is
GCF of Numerators i.e. for 670,140 is 10
LCM of denominators i.e. for 81,217 is 17577.
Thus, GCF of Fractions is 10/17577.Finally, GCF of Fractions for 670/81, 140/217 is 10/17577.