GCF of 396/870, 321/419
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 396/870, 321/419 i.e 3/364530 easily. The following is the detailed procedure to determine the greatest common factor of fractions 396/870, 321/419.
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 396/870,321/419?
Given fractions are 396/870,321/419
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 396/870,321/419, numerators are 396,321
Denominators are 870,419
The GCF of 396,321 is 3 .
LCM of 870,419 is 364530.
The greatest common factor of 396/870,321/419 = [GCF of 396,321]/[LCM of 870,419]= 3/364530
Therefore, the GCF of 396/870,321/419 is 3/364530.
To find the highest common factor of 396,321, we have to find the factors of both numbers and list the highest common factor.
The factors of 396 are 1, 2, 3, 4, 6, 9, 11, 12, 18, 22, 33, 36, 44, 66, 99, 132, 198, 396
The factors of 321 are 1, 3, 107, 321
The HCF of 396,321 is 3.
Lets's calculate GCF of 396,321
| 3 | 396, 321 |
| 132, 107 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 396,321 By Matching Biggest Common Factor Method
Now, list down the factors of 396
:1,2,3,4,6,9,11,12,18,22,33,36,44,66,99,132,198,396
Now, list down the factors of 321
:1,3,107,321
Greatest Common Factor
We found the factors 396,321 . The biggest common factor number is the GCF number.
So the greatest common factor 396,321 is 3.
Lets's calculate LCM of 870,419
Given numbers has no common factors except 1. So, there LCM is their product i.e 364530
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/364530
Therefore, the GCF of Fractions 396/870,321/419 is 3/364530
Least Common Multiple of 870,419 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 870,419 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(870,419) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(870,419) x common factors =1 x 1 = 1
LCM(870,419) = ( 870 × 419 ) / 1
LCM(870,419) = 364530 / 1
LCM(870,419) = 364530
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FAQs on GCF of Fractions of 396/870, 321/419
1. What is the HCF of 396,321?
The HCF of 396,321 is 3
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 396/870, 321/419?
Answer: GCF of Numerators as per given numbers 396/870, 321/419 is
GCF of Numerators i.e. for 396,321 is 3
LCM of denominators i.e. for 870,419 is 364530.
Thus, GCF of Fractions is 3/364530.Finally, GCF of Fractions for 396/870, 321/419 is 3/364530.