GCF of 560/342, 416/112, 766/189
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 560/342, 416/112, 766/189 i.e 2/57456 easily. The following is the detailed procedure to determine the greatest common factor of fractions 560/342, 416/112, 766/189.
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 560/342,416/112,766/189?
Given fractions are 560/342,416/112,766/189
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 560/342,416/112,766/189, numerators are 560,416,766
Denominators are 342,112,189
The GCF of 560,416,766 is 2 .
LCM of 342,112,189 is 57456.
The greatest common factor of 560/342,416/112,766/189 = [GCF of 560,416,766]/[LCM of 342,112,189]= 2/57456
Therefore, the GCF of 560/342,416/112,766/189 is 2/57456.
To find the highest common factor of 560,416,766, we have to find the factors of both numbers and list the highest common factor.
The factors of 560 are 1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 28, 35, 40, 56, 70, 80, 112, 140, 280, 560
The factors of 416 are 1, 2, 4, 8, 13, 16, 26, 32, 52, 104, 208, 416
The factors of 766 are 1, 2, 383, 766
The HCF of 560,416,766 is 2.
Lets's calculate GCF of 560,416,766
| 2 | 560, 416, 766 |
| 280, 208, 383 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 560,416,766 By Matching Biggest Common Factor Method
Now, list down the factors of 560
:1,2,4,5,7,8,10,14,16,20,28,35,40,56,70,80,112,140,280,560
Now, list down the factors of 416
:1,2,4,8,13,16,26,32,52,104,208,416
Now, list down the factors of 766
:1,2,383,766
Greatest Common Factor
We found the factors 560,416,766 . The biggest common factor number is the GCF number.
So the greatest common factor 560,416,766 is 2.
Lets's calculate LCM of 342,112,189
| 2 | 342, 112, 189 |
| 3 | 171, 56, 189 |
| 3 | 57, 56, 63 |
| 7 | 19, 56, 21 |
| 19, 8, 3 |
∴ So the LCM of the given numbers is 2 x 3 x 3 x 7 x 19 x 8 x 3 = 57456
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/57456
Therefore, the GCF of Fractions 560/342,416/112,766/189 is 2/57456
Least Common Multiple of 342,112,189 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 342,112,189 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(342,112,189) = 1
common factors(in case of two or more numbers have common factors) = 126
GCF(342,112,189) x common factors =1 x 126 = 126
LCM(342,112,189) = ( 342 × 112 × 189 ) / 126
LCM(342,112,189) = 7239456 / 126
LCM(342,112,189) = 57456
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 560/342, 416/112, 766/189
1. What is the HCF of 560,416,766?
The HCF of 560,416,766 is 2
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 560/342, 416/112, 766/189?
Answer: GCF of Numerators as per given numbers 560/342, 416/112, 766/189 is
GCF of Numerators i.e. for 560,416,766 is 2
LCM of denominators i.e. for 342,112,189 is 57456.
Thus, GCF of Fractions is 2/57456.Finally, GCF of Fractions for 560/342, 416/112, 766/189 is 2/57456.