GCF of 868/470, 3206/416
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 868/470, 3206/416 i.e 14/97760 easily. The following is the detailed procedure to determine the greatest common factor of fractions 868/470, 3206/416.
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 868/470,3206/416?
Given fractions are 868/470,3206/416
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 868/470,3206/416, numerators are 868,3206
Denominators are 470,416
The GCF of 868,3206 is 14 .
LCM of 470,416 is 97760.
The greatest common factor of 868/470,3206/416 = [GCF of 868,3206]/[LCM of 470,416]= 14/97760
Therefore, the GCF of 868/470,3206/416 is 14/97760.
To find the highest common factor of 868,3206, we have to find the factors of both numbers and list the highest common factor.
The factors of 868 are 1, 2, 4, 7, 14, 28, 31, 62, 124, 217, 434, 868
The factors of 3206 are 1, 2, 7, 14, 229, 458, 1603, 3206
The HCF of 868,3206 is 14.
Lets's calculate GCF of 868,3206
| 2 | 868, 3206 |
| 7 | 434, 1603 |
| 62, 229 |
∴ So the GCF of the given numbers is 2 x 7 = 14
Greatest Common Factor of 868,3206 By Matching Biggest Common Factor Method
Now, list down the factors of 868
:1,2,4,7,14,28,31,62,124,217,434,868
Now, list down the factors of 3206
:1,2,7,14,229,458,1603,3206
Greatest Common Factor
We found the factors 868,3206 . The biggest common factor number is the GCF number.
So the greatest common factor 868,3206 is 14.
Lets's calculate LCM of 470,416
| 2 | 470, 416 |
| 235, 208 |
∴ So the LCM of the given numbers is 2 x 235 x 208 = 97760
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 14/97760
Therefore, the GCF of Fractions 868/470,3206/416 is 14/97760
Least Common Multiple of 470,416 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 470,416 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(470,416) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(470,416) x common factors =2 x 1 = 2
LCM(470,416) = ( 470 × 416 ) / 2
LCM(470,416) = 195520 / 2
LCM(470,416) = 97760
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FAQs on GCF of Fractions of 868/470, 3206/416
1. What is the HCF of 868,3206?
The HCF of 868,3206 is 14
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 868/470, 3206/416?
Answer: GCF of Numerators as per given numbers 868/470, 3206/416 is
GCF of Numerators i.e. for 868,3206 is 14
LCM of denominators i.e. for 470,416 is 97760.
Thus, GCF of Fractions is 14/97760.Finally, GCF of Fractions for 868/470, 3206/416 is 14/97760.