GCF of 289/712, 280/134
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 289/712, 280/134 i.e 1/47704 easily. The following is the detailed procedure to determine the greatest common factor of fractions 289/712, 280/134.
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 289/712,280/134?
Given fractions are 289/712,280/134
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 289/712,280/134, numerators are 289,280
Denominators are 712,134
The GCF of 289,280 is 1 .
LCM of 712,134 is 47704.
The greatest common factor of 289/712,280/134 = [GCF of 289,280]/[LCM of 712,134]= 1/47704
Therefore, the GCF of 289/712,280/134 is 1/47704.
To find the highest common factor of 289,280, we have to find the factors of both numbers and list the highest common factor.
The factors of 289 are 1, 17, 289
The factors of 280 are 1, 2, 4, 5, 7, 8, 10, 14, 20, 28, 35, 40, 56, 70, 140, 280
The HCF of 289,280 is 1.
Lets's calculate GCF of 289,280
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 289,280 By Matching Biggest Common Factor Method
Now, list down the factors of 289
:1,17,289
Now, list down the factors of 280
:1,2,4,5,7,8,10,14,20,28,35,40,56,70,140,280
Greatest Common Factor
We found the factors 289,280 . The biggest common factor number is the GCF number.
So the greatest common factor 289,280 is 1.
Lets's calculate LCM of 712,134
| 2 | 712, 134 |
| 356, 67 |
∴ So the LCM of the given numbers is 2 x 356 x 67 = 47704
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/47704
Therefore, the GCF of Fractions 289/712,280/134 is 1/47704
Least Common Multiple of 712,134 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 712,134 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(712,134) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(712,134) x common factors =2 x 1 = 2
LCM(712,134) = ( 712 × 134 ) / 2
LCM(712,134) = 95408 / 2
LCM(712,134) = 47704
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FAQs on GCF of Fractions of 289/712, 280/134
1. What is the HCF of 289,280?
The HCF of 289,280 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 289/712, 280/134?
Answer: GCF of Numerators as per given numbers 289/712, 280/134 is
GCF of Numerators i.e. for 289,280 is 1
LCM of denominators i.e. for 712,134 is 47704.
Thus, GCF of Fractions is 1/47704.Finally, GCF of Fractions for 289/712, 280/134 is 1/47704.