GCF of 5751/896, 3678/3000
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 5751/896, 3678/3000 i.e 3/336000 easily. The following is the detailed procedure to determine the greatest common factor of fractions 5751/896, 3678/3000.
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 5751/896,3678/3000?
Given fractions are 5751/896,3678/3000
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 5751/896,3678/3000, numerators are 5751,3678
Denominators are 896,3000
The GCF of 5751,3678 is 3 .
LCM of 896,3000 is 336000.
The greatest common factor of 5751/896,3678/3000 = [GCF of 5751,3678]/[LCM of 896,3000]= 3/336000
Therefore, the GCF of 5751/896,3678/3000 is 3/336000.
To find the highest common factor of 5751,3678, we have to find the factors of both numbers and list the highest common factor.
The factors of 5751 are 1, 3, 9, 27, 71, 81, 213, 639, 1917, 5751
The factors of 3678 are 1, 2, 3, 6, 613, 1226, 1839, 3678
The HCF of 5751,3678 is 3.
Lets's calculate GCF of 5751,3678
| 3 | 5751, 3678 |
| 1917, 1226 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 5751,3678 By Matching Biggest Common Factor Method
Now, list down the factors of 5751
:1,3,9,27,71,81,213,639,1917,5751
Now, list down the factors of 3678
:1,2,3,6,613,1226,1839,3678
Greatest Common Factor
We found the factors 5751,3678 . The biggest common factor number is the GCF number.
So the greatest common factor 5751,3678 is 3.
Lets's calculate LCM of 896,3000
| 2 | 896, 3000 |
| 2 | 448, 1500 |
| 2 | 224, 750 |
| 112, 375 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 112 x 375 = 336000
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/336000
Therefore, the GCF of Fractions 5751/896,3678/3000 is 3/336000
Least Common Multiple of 896,3000 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 896,3000 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(896,3000) = 8
common factors(in case of two or more numbers have common factors) = 1
GCF(896,3000) x common factors =8 x 1 = 8
LCM(896,3000) = ( 896 × 3000 ) / 8
LCM(896,3000) = 2688000 / 8
LCM(896,3000) = 336000
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FAQs on GCF of Fractions of 5751/896, 3678/3000
1. What is the HCF of 5751,3678?
The HCF of 5751,3678 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 5751/896, 3678/3000?
Answer: GCF of Numerators as per given numbers 5751/896, 3678/3000 is
GCF of Numerators i.e. for 5751,3678 is 3
LCM of denominators i.e. for 896,3000 is 336000.
Thus, GCF of Fractions is 3/336000.Finally, GCF of Fractions for 5751/896, 3678/3000 is 3/336000.