GCF of 5670/870, 5768/4029
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 5670/870, 5768/4029 i.e 14/1168410 easily. The following is the detailed procedure to determine the greatest common factor of fractions 5670/870, 5768/4029.
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 5670/870,5768/4029?
Given fractions are 5670/870,5768/4029
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 5670/870,5768/4029, numerators are 5670,5768
Denominators are 870,4029
The GCF of 5670,5768 is 14 .
LCM of 870,4029 is 1168410.
The greatest common factor of 5670/870,5768/4029 = [GCF of 5670,5768]/[LCM of 870,4029]= 14/1168410
Therefore, the GCF of 5670/870,5768/4029 is 14/1168410.
To find the highest common factor of 5670,5768, we have to find the factors of both numbers and list the highest common factor.
The factors of 5670 are 1, 2, 3, 5, 6, 7, 9, 10, 14, 15, 18, 21, 27, 30, 35, 42, 45, 54, 63, 70, 81, 90, 105, 126, 135, 162, 189, 210, 270, 315, 378, 405, 567, 630, 810, 945, 1134, 1890, 2835, 5670
The factors of 5768 are 1, 2, 4, 7, 8, 14, 28, 56, 103, 206, 412, 721, 824, 1442, 2884, 5768
The HCF of 5670,5768 is 14.
Lets's calculate GCF of 5670,5768
| 2 | 5670, 5768 |
| 7 | 2835, 2884 |
| 405, 412 |
∴ So the GCF of the given numbers is 2 x 7 = 14
Greatest Common Factor of 5670,5768 By Matching Biggest Common Factor Method
Now, list down the factors of 5670
:1,2,3,5,6,7,9,10,14,15,18,21,27,30,35,42,45,54,63,70,81,90,105,126,135,162,189,210,270,315,378,405,567,630,810,945,1134,1890,2835,5670
Now, list down the factors of 5768
:1,2,4,7,8,14,28,56,103,206,412,721,824,1442,2884,5768
Greatest Common Factor
We found the factors 5670,5768 . The biggest common factor number is the GCF number.
So the greatest common factor 5670,5768 is 14.
Lets's calculate LCM of 870,4029
| 3 | 870, 4029 |
| 290, 1343 |
∴ So the LCM of the given numbers is 3 x 290 x 1343 = 1168410
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 14/1168410
Therefore, the GCF of Fractions 5670/870,5768/4029 is 14/1168410
Least Common Multiple of 870,4029 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 870,4029 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(870,4029) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(870,4029) x common factors =3 x 1 = 3
LCM(870,4029) = ( 870 × 4029 ) / 3
LCM(870,4029) = 3505230 / 3
LCM(870,4029) = 1168410
GCF of Fractions Calculation Examples
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FAQs on GCF of Fractions of 5670/870, 5768/4029
1. What is the HCF of 5670,5768?
The HCF of 5670,5768 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 5670/870, 5768/4029?
Answer: GCF of Numerators as per given numbers 5670/870, 5768/4029 is
GCF of Numerators i.e. for 5670,5768 is 14
LCM of denominators i.e. for 870,4029 is 1168410.
Thus, GCF of Fractions is 14/1168410.Finally, GCF of Fractions for 5670/870, 5768/4029 is 14/1168410.