GCF of 8142/754, 2143/1780
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 8142/754, 2143/1780 i.e 1/671060 easily. The following is the detailed procedure to determine the greatest common factor of fractions 8142/754, 2143/1780.
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 8142/754,2143/1780?
Given fractions are 8142/754,2143/1780
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 8142/754,2143/1780, numerators are 8142,2143
Denominators are 754,1780
The GCF of 8142,2143 is 1 .
LCM of 754,1780 is 671060.
The greatest common factor of 8142/754,2143/1780 = [GCF of 8142,2143]/[LCM of 754,1780]= 1/671060
Therefore, the GCF of 8142/754,2143/1780 is 1/671060.
To find the highest common factor of 8142,2143, we have to find the factors of both numbers and list the highest common factor.
The factors of 8142 are 1, 2, 3, 6, 23, 46, 59, 69, 118, 138, 177, 354, 1357, 2714, 4071, 8142
The factors of 2143 are 1, 2143
The HCF of 8142,2143 is 1.
Lets's calculate GCF of 8142,2143
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 8142,2143 By Matching Biggest Common Factor Method
Now, list down the factors of 8142
:1,2,3,6,23,46,59,69,118,138,177,354,1357,2714,4071,8142
Now, list down the factors of 2143
:1,2143
Greatest Common Factor
We found the factors 8142,2143 . The biggest common factor number is the GCF number.
So the greatest common factor 8142,2143 is 1.
Lets's calculate LCM of 754,1780
| 2 | 754, 1780 |
| 377, 890 |
∴ So the LCM of the given numbers is 2 x 377 x 890 = 671060
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/671060
Therefore, the GCF of Fractions 8142/754,2143/1780 is 1/671060
Least Common Multiple of 754,1780 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 754,1780 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(754,1780) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(754,1780) x common factors =2 x 1 = 2
LCM(754,1780) = ( 754 × 1780 ) / 2
LCM(754,1780) = 1342120 / 2
LCM(754,1780) = 671060
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FAQs on GCF of Fractions of 8142/754, 2143/1780
1. What is the HCF of 8142,2143?
The HCF of 8142,2143 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 8142/754, 2143/1780?
Answer: GCF of Numerators as per given numbers 8142/754, 2143/1780 is
GCF of Numerators i.e. for 8142,2143 is 1
LCM of denominators i.e. for 754,1780 is 671060.
Thus, GCF of Fractions is 1/671060.Finally, GCF of Fractions for 8142/754, 2143/1780 is 1/671060.