GCF of 3780/515, 5214/4043
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 3780/515, 5214/4043 i.e 6/2082145 easily. The following is the detailed procedure to determine the greatest common factor of fractions 3780/515, 5214/4043.
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 3780/515,5214/4043?
Given fractions are 3780/515,5214/4043
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 3780/515,5214/4043, numerators are 3780,5214
Denominators are 515,4043
The GCF of 3780,5214 is 6 .
LCM of 515,4043 is 2082145.
The greatest common factor of 3780/515,5214/4043 = [GCF of 3780,5214]/[LCM of 515,4043]= 6/2082145
Therefore, the GCF of 3780/515,5214/4043 is 6/2082145.
To find the highest common factor of 3780,5214, we have to find the factors of both numbers and list the highest common factor.
The factors of 3780 are 1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 14, 15, 18, 20, 21, 27, 28, 30, 35, 36, 42, 45, 54, 60, 63, 70, 84, 90, 105, 108, 126, 135, 140, 180, 189, 210, 252, 270, 315, 378, 420, 540, 630, 756, 945, 1260, 1890, 3780
The factors of 5214 are 1, 2, 3, 6, 11, 22, 33, 66, 79, 158, 237, 474, 869, 1738, 2607, 5214
The HCF of 3780,5214 is 6.
Lets's calculate GCF of 3780,5214
| 2 | 3780, 5214 |
| 3 | 1890, 2607 |
| 630, 869 |
∴ So the GCF of the given numbers is 2 x 3 = 6
Greatest Common Factor of 3780,5214 By Matching Biggest Common Factor Method
Now, list down the factors of 3780
:1,2,3,4,5,6,7,9,10,12,14,15,18,20,21,27,28,30,35,36,42,45,54,60,63,70,84,90,105,108,126,135,140,180,189,210,252,270,315,378,420,540,630,756,945,1260,1890,3780
Now, list down the factors of 5214
:1,2,3,6,11,22,33,66,79,158,237,474,869,1738,2607,5214
Greatest Common Factor
We found the factors 3780,5214 . The biggest common factor number is the GCF number.
So the greatest common factor 3780,5214 is 6.
Lets's calculate LCM of 515,4043
Given numbers has no common factors except 1. So, there LCM is their product i.e 2082145
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/2082145
Therefore, the GCF of Fractions 3780/515,5214/4043 is 6/2082145
Least Common Multiple of 515,4043 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 515,4043 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(515,4043) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(515,4043) x common factors =1 x 1 = 1
LCM(515,4043) = ( 515 × 4043 ) / 1
LCM(515,4043) = 2082145 / 1
LCM(515,4043) = 2082145
GCF of Fractions Calculation Examples
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FAQs on GCF of Fractions of 3780/515, 5214/4043
1. What is the HCF of 3780,5214?
The HCF of 3780,5214 is 6
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 3780/515, 5214/4043?
Answer: GCF of Numerators as per given numbers 3780/515, 5214/4043 is
GCF of Numerators i.e. for 3780,5214 is 6
LCM of denominators i.e. for 515,4043 is 2082145.
Thus, GCF of Fractions is 6/2082145.Finally, GCF of Fractions for 3780/515, 5214/4043 is 6/2082145.