GCF of 2139/678, 1159/7784
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 2139/678, 1159/7784 i.e 1/2638776 easily. The following is the detailed procedure to determine the greatest common factor of fractions 2139/678, 1159/7784.
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 2139/678,1159/7784?
Given fractions are 2139/678,1159/7784
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 2139/678,1159/7784, numerators are 2139,1159
Denominators are 678,7784
The GCF of 2139,1159 is 1 .
LCM of 678,7784 is 2638776.
The greatest common factor of 2139/678,1159/7784 = [GCF of 2139,1159]/[LCM of 678,7784]= 1/2638776
Therefore, the GCF of 2139/678,1159/7784 is 1/2638776.
To find the highest common factor of 2139,1159, we have to find the factors of both numbers and list the highest common factor.
The factors of 2139 are 1, 3, 23, 31, 69, 93, 713, 2139
The factors of 1159 are 1, 19, 61, 1159
The HCF of 2139,1159 is 1.
Lets's calculate GCF of 2139,1159
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 2139,1159 By Matching Biggest Common Factor Method
Now, list down the factors of 2139
:1,3,23,31,69,93,713,2139
Now, list down the factors of 1159
:1,19,61,1159
Greatest Common Factor
We found the factors 2139,1159 . The biggest common factor number is the GCF number.
So the greatest common factor 2139,1159 is 1.
Lets's calculate LCM of 678,7784
| 2 | 678, 7784 |
| 339, 3892 |
∴ So the LCM of the given numbers is 2 x 339 x 3892 = 2638776
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/2638776
Therefore, the GCF of Fractions 2139/678,1159/7784 is 1/2638776
Least Common Multiple of 678,7784 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 678,7784 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(678,7784) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(678,7784) x common factors =2 x 1 = 2
LCM(678,7784) = ( 678 × 7784 ) / 2
LCM(678,7784) = 5277552 / 2
LCM(678,7784) = 2638776
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FAQs on GCF of Fractions of 2139/678, 1159/7784
1. What is the HCF of 2139,1159?
The HCF of 2139,1159 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 2139/678, 1159/7784?
Answer: GCF of Numerators as per given numbers 2139/678, 1159/7784 is
GCF of Numerators i.e. for 2139,1159 is 1
LCM of denominators i.e. for 678,7784 is 2638776.
Thus, GCF of Fractions is 1/2638776.Finally, GCF of Fractions for 2139/678, 1159/7784 is 1/2638776.