GCF of 3945/429, 8538/3978
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 3945/429, 8538/3978 i.e 3/43758 easily. The following is the detailed procedure to determine the greatest common factor of fractions 3945/429, 8538/3978.
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 3945/429,8538/3978?
Given fractions are 3945/429,8538/3978
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 3945/429,8538/3978, numerators are 3945,8538
Denominators are 429,3978
The GCF of 3945,8538 is 3 .
LCM of 429,3978 is 43758.
The greatest common factor of 3945/429,8538/3978 = [GCF of 3945,8538]/[LCM of 429,3978]= 3/43758
Therefore, the GCF of 3945/429,8538/3978 is 3/43758.
To find the highest common factor of 3945,8538, we have to find the factors of both numbers and list the highest common factor.
The factors of 3945 are 1, 3, 5, 15, 263, 789, 1315, 3945
The factors of 8538 are 1, 2, 3, 6, 1423, 2846, 4269, 8538
The HCF of 3945,8538 is 3.
Lets's calculate GCF of 3945,8538
| 3 | 3945, 8538 |
| 1315, 2846 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 3945,8538 By Matching Biggest Common Factor Method
Now, list down the factors of 3945
:1,3,5,15,263,789,1315,3945
Now, list down the factors of 8538
:1,2,3,6,1423,2846,4269,8538
Greatest Common Factor
We found the factors 3945,8538 . The biggest common factor number is the GCF number.
So the greatest common factor 3945,8538 is 3.
Lets's calculate LCM of 429,3978
| 3 | 429, 3978 |
| 13 | 143, 1326 |
| 11, 102 |
∴ So the LCM of the given numbers is 3 x 13 x 11 x 102 = 43758
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/43758
Therefore, the GCF of Fractions 3945/429,8538/3978 is 3/43758
Least Common Multiple of 429,3978 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 429,3978 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(429,3978) = 39
common factors(in case of two or more numbers have common factors) = 1
GCF(429,3978) x common factors =39 x 1 = 39
LCM(429,3978) = ( 429 × 3978 ) / 39
LCM(429,3978) = 1706562 / 39
LCM(429,3978) = 43758
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FAQs on GCF of Fractions of 3945/429, 8538/3978
1. What is the HCF of 3945,8538?
The HCF of 3945,8538 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 3945/429, 8538/3978?
Answer: GCF of Numerators as per given numbers 3945/429, 8538/3978 is
GCF of Numerators i.e. for 3945,8538 is 3
LCM of denominators i.e. for 429,3978 is 43758.
Thus, GCF of Fractions is 3/43758.Finally, GCF of Fractions for 3945/429, 8538/3978 is 3/43758.