GCF of 410/39, 210/546
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 410/39, 210/546 i.e 10/546 easily. The following is the detailed procedure to determine the greatest common factor of fractions 410/39, 210/546.
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 410/39,210/546?
Given fractions are 410/39,210/546
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 410/39,210/546, numerators are 410,210
Denominators are 39,546
The GCF of 410,210 is 10 .
LCM of 39,546 is 546.
The greatest common factor of 410/39,210/546 = [GCF of 410,210]/[LCM of 39,546]= 10/546
Therefore, the GCF of 410/39,210/546 is 10/546.
To find the highest common factor of 410,210, we have to find the factors of both numbers and list the highest common factor.
The factors of 410 are 1, 2, 5, 10, 41, 82, 205, 410
The factors of 210 are 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 210
The HCF of 410,210 is 10.
Lets's calculate GCF of 410,210
| 2 | 410, 210 |
| 5 | 205, 105 |
| 41, 21 |
∴ So the GCF of the given numbers is 2 x 5 = 10
Greatest Common Factor of 410,210 By Matching Biggest Common Factor Method
Now, list down the factors of 410
:1,2,5,10,41,82,205,410
Now, list down the factors of 210
:1,2,3,5,6,7,10,14,15,21,30,35,42,70,105,210
Greatest Common Factor
We found the factors 410,210 . The biggest common factor number is the GCF number.
So the greatest common factor 410,210 is 10.
Lets's calculate LCM of 39,546
| 3 | 39, 546 |
| 13 | 13, 182 |
| 1, 14 |
∴ So the LCM of the given numbers is 3 x 13 x 1 x 14 = 546
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 10/546
Therefore, the GCF of Fractions 410/39,210/546 is 10/546
Least Common Multiple of 39,546 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 39,546 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(39,546) = 39
common factors(in case of two or more numbers have common factors) = 1
GCF(39,546) x common factors =39 x 1 = 39
LCM(39,546) = ( 39 × 546 ) / 39
LCM(39,546) = 21294 / 39
LCM(39,546) = 546
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FAQs on GCF of Fractions of 410/39, 210/546
1. What is the HCF of 410,210?
The HCF of 410,210 is 10
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 410/39, 210/546?
Answer: GCF of Numerators as per given numbers 410/39, 210/546 is
GCF of Numerators i.e. for 410,210 is 10
LCM of denominators i.e. for 39,546 is 546.
Thus, GCF of Fractions is 10/546.Finally, GCF of Fractions for 410/39, 210/546 is 10/546.