GCF of 43/40, 870/51, 210/256
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 43/40, 870/51, 210/256 i.e 1/65280 easily. The following is the detailed procedure to determine the greatest common factor of fractions 43/40, 870/51, 210/256.
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 43/40,870/51,210/256?
Given fractions are 43/40,870/51,210/256
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 43/40,870/51,210/256, numerators are 43,870,210
Denominators are 40,51,256
The GCF of 43,870,210 is 1 .
LCM of 40,51,256 is 65280.
The greatest common factor of 43/40,870/51,210/256 = [GCF of 43,870,210]/[LCM of 40,51,256]= 1/65280
Therefore, the GCF of 43/40,870/51,210/256 is 1/65280.
To find the highest common factor of 43,870,210, we have to find the factors of both numbers and list the highest common factor.
The factors of 43 are 1, 43
The factors of 870 are 1, 2, 3, 5, 6, 10, 15, 29, 30, 58, 87, 145, 174, 290, 435, 870
The factors of 210 are 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 210
The HCF of 43,870,210 is 1.
Lets's calculate GCF of 43,870,210
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 43,870,210 By Matching Biggest Common Factor Method
Now, list down the factors of 43
:1,43
Now, list down the factors of 870
:1,2,3,5,6,10,15,29,30,58,87,145,174,290,435,870
Now, list down the factors of 210
:1,2,3,5,6,7,10,14,15,21,30,35,42,70,105,210
Greatest Common Factor
We found the factors 43,870,210 . The biggest common factor number is the GCF number.
So the greatest common factor 43,870,210 is 1.
Lets's calculate LCM of 40,51,256
| 2 | 40, 51, 256 |
| 2 | 20, 51, 128 |
| 2 | 10, 51, 64 |
| 5, 51, 32 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 5 x 51 x 32 = 65280
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/65280
Therefore, the GCF of Fractions 43/40,870/51,210/256 is 1/65280
Least Common Multiple of 40,51,256 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 40,51,256 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(40,51,256) = 1
common factors(in case of two or more numbers have common factors) = 8
GCF(40,51,256) x common factors =1 x 8 = 8
LCM(40,51,256) = ( 40 × 51 × 256 ) / 8
LCM(40,51,256) = 522240 / 8
LCM(40,51,256) = 65280
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FAQs on GCF of Fractions of 43/40, 870/51, 210/256
1. What is the HCF of 43,870,210?
The HCF of 43,870,210 is 1
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 43/40, 870/51, 210/256?
Answer: GCF of Numerators as per given numbers 43/40, 870/51, 210/256 is
GCF of Numerators i.e. for 43,870,210 is 1
LCM of denominators i.e. for 40,51,256 is 65280.
Thus, GCF of Fractions is 1/65280.Finally, GCF of Fractions for 43/40, 870/51, 210/256 is 1/65280.