GCF of 147/170, 322/419
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 147/170, 322/419 i.e 7/71230 easily. The following is the detailed procedure to determine the greatest common factor of fractions 147/170, 322/419.
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 147/170,322/419?
Given fractions are 147/170,322/419
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 147/170,322/419, numerators are 147,322
Denominators are 170,419
The GCF of 147,322 is 7 .
LCM of 170,419 is 71230.
The greatest common factor of 147/170,322/419 = [GCF of 147,322]/[LCM of 170,419]= 7/71230
Therefore, the GCF of 147/170,322/419 is 7/71230.
To find the highest common factor of 147,322, we have to find the factors of both numbers and list the highest common factor.
The factors of 147 are 1, 3, 7, 21, 49, 147
The factors of 322 are 1, 2, 7, 14, 23, 46, 161, 322
The HCF of 147,322 is 7.
Lets's calculate GCF of 147,322
| 7 | 147, 322 |
| 21, 46 |
∴ So the GCF of the given numbers is 7 = 7
Greatest Common Factor of 147,322 By Matching Biggest Common Factor Method
Now, list down the factors of 147
:1,3,7,21,49,147
Now, list down the factors of 322
:1,2,7,14,23,46,161,322
Greatest Common Factor
We found the factors 147,322 . The biggest common factor number is the GCF number.
So the greatest common factor 147,322 is 7.
Lets's calculate LCM of 170,419
Given numbers has no common factors except 1. So, there LCM is their product i.e 71230
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 7/71230
Therefore, the GCF of Fractions 147/170,322/419 is 7/71230
Least Common Multiple of 170,419 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 170,419 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(170,419) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(170,419) x common factors =1 x 1 = 1
LCM(170,419) = ( 170 × 419 ) / 1
LCM(170,419) = 71230 / 1
LCM(170,419) = 71230
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 147/170, 322/419
1. What is the HCF of 147,322?
The HCF of 147,322 is 7
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 147/170, 322/419?
Answer: GCF of Numerators as per given numbers 147/170, 322/419 is
GCF of Numerators i.e. for 147,322 is 7
LCM of denominators i.e. for 170,419 is 71230.
Thus, GCF of Fractions is 7/71230.Finally, GCF of Fractions for 147/170, 322/419 is 7/71230.