GCF of 409/977, 3478/319
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 409/977, 3478/319 i.e 1/311663 easily. The following is the detailed procedure to determine the greatest common factor of fractions 409/977, 3478/319.
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 409/977,3478/319?
Given fractions are 409/977,3478/319
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 409/977,3478/319, numerators are 409,3478
Denominators are 977,319
The GCF of 409,3478 is 1 .
LCM of 977,319 is 311663.
The greatest common factor of 409/977,3478/319 = [GCF of 409,3478]/[LCM of 977,319]= 1/311663
Therefore, the GCF of 409/977,3478/319 is 1/311663.
To find the highest common factor of 409,3478, we have to find the factors of both numbers and list the highest common factor.
The factors of 409 are 1, 409
The factors of 3478 are 1, 2, 37, 47, 74, 94, 1739, 3478
The HCF of 409,3478 is 1.
Lets's calculate GCF of 409,3478
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 409,3478 By Matching Biggest Common Factor Method
Now, list down the factors of 409
:1,409
Now, list down the factors of 3478
:1,2,37,47,74,94,1739,3478
Greatest Common Factor
We found the factors 409,3478 . The biggest common factor number is the GCF number.
So the greatest common factor 409,3478 is 1.
Lets's calculate LCM of 977,319
Given numbers has no common factors except 1. So, there LCM is their product i.e 311663
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/311663
Therefore, the GCF of Fractions 409/977,3478/319 is 1/311663
Least Common Multiple of 977,319 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 977,319 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(977,319) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(977,319) x common factors =1 x 1 = 1
LCM(977,319) = ( 977 × 319 ) / 1
LCM(977,319) = 311663 / 1
LCM(977,319) = 311663
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 409/977, 3478/319
1. What is the HCF of 409,3478?
The HCF of 409,3478 is 1
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 409/977, 3478/319?
Answer: GCF of Numerators as per given numbers 409/977, 3478/319 is
GCF of Numerators i.e. for 409,3478 is 1
LCM of denominators i.e. for 977,319 is 311663.
Thus, GCF of Fractions is 1/311663.Finally, GCF of Fractions for 409/977, 3478/319 is 1/311663.