GCF of 155/97, 217/214
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 155/97, 217/214 i.e 31/20758 easily. The following is the detailed procedure to determine the greatest common factor of fractions 155/97, 217/214.
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 155/97,217/214?
Given fractions are 155/97,217/214
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 155/97,217/214, numerators are 155,217
Denominators are 97,214
The GCF of 155,217 is 31 .
LCM of 97,214 is 20758.
The greatest common factor of 155/97,217/214 = [GCF of 155,217]/[LCM of 97,214]= 31/20758
Therefore, the GCF of 155/97,217/214 is 31/20758.
To find the highest common factor of 155,217, we have to find the factors of both numbers and list the highest common factor.
The factors of 155 are 1, 5, 31, 155
The factors of 217 are 1, 7, 31, 217
The HCF of 155,217 is 31.
Lets's calculate GCF of 155,217
| 31 | 155, 217 |
| 5, 7 |
∴ So the GCF of the given numbers is 31 = 31
Greatest Common Factor of 155,217 By Matching Biggest Common Factor Method
Now, list down the factors of 155
:1,5,31,155
Now, list down the factors of 217
:1,7,31,217
Greatest Common Factor
We found the factors 155,217 . The biggest common factor number is the GCF number.
So the greatest common factor 155,217 is 31.
Lets's calculate LCM of 97,214
Given numbers has no common factors except 1. So, there LCM is their product i.e 20758
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 31/20758
Therefore, the GCF of Fractions 155/97,217/214 is 31/20758
Least Common Multiple of 97,214 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 97,214 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(97,214) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(97,214) x common factors =1 x 1 = 1
LCM(97,214) = ( 97 × 214 ) / 1
LCM(97,214) = 20758 / 1
LCM(97,214) = 20758
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 155/97, 217/214
1. What is the HCF of 155,217?
The HCF of 155,217 is 31
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 155/97, 217/214?
Answer: GCF of Numerators as per given numbers 155/97, 217/214 is
GCF of Numerators i.e. for 155,217 is 31
LCM of denominators i.e. for 97,214 is 20758.
Thus, GCF of Fractions is 31/20758.Finally, GCF of Fractions for 155/97, 217/214 is 31/20758.