GCF of 646/561, 5414/419
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 646/561, 5414/419 i.e 2/235059 easily. The following is the detailed procedure to determine the greatest common factor of fractions 646/561, 5414/419.
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 646/561,5414/419?
Given fractions are 646/561,5414/419
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 646/561,5414/419, numerators are 646,5414
Denominators are 561,419
The GCF of 646,5414 is 2 .
LCM of 561,419 is 235059.
The greatest common factor of 646/561,5414/419 = [GCF of 646,5414]/[LCM of 561,419]= 2/235059
Therefore, the GCF of 646/561,5414/419 is 2/235059.
To find the highest common factor of 646,5414, we have to find the factors of both numbers and list the highest common factor.
The factors of 646 are 1, 2, 17, 19, 34, 38, 323, 646
The factors of 5414 are 1, 2, 2707, 5414
The HCF of 646,5414 is 2.
Lets's calculate GCF of 646,5414
| 2 | 646, 5414 |
| 323, 2707 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 646,5414 By Matching Biggest Common Factor Method
Now, list down the factors of 646
:1,2,17,19,34,38,323,646
Now, list down the factors of 5414
:1,2,2707,5414
Greatest Common Factor
We found the factors 646,5414 . The biggest common factor number is the GCF number.
So the greatest common factor 646,5414 is 2.
Lets's calculate LCM of 561,419
Given numbers has no common factors except 1. So, there LCM is their product i.e 235059
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/235059
Therefore, the GCF of Fractions 646/561,5414/419 is 2/235059
Least Common Multiple of 561,419 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 561,419 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(561,419) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(561,419) x common factors =1 x 1 = 1
LCM(561,419) = ( 561 × 419 ) / 1
LCM(561,419) = 235059 / 1
LCM(561,419) = 235059
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FAQs on GCF of Fractions of 646/561, 5414/419
1. What is the HCF of 646,5414?
The HCF of 646,5414 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 646/561, 5414/419?
Answer: GCF of Numerators as per given numbers 646/561, 5414/419 is
GCF of Numerators i.e. for 646,5414 is 2
LCM of denominators i.e. for 561,419 is 235059.
Thus, GCF of Fractions is 2/235059.Finally, GCF of Fractions for 646/561, 5414/419 is 2/235059.