Use our free GCF of Fractions Calculator tool to compute the GCF of 1656/434, 6900/6560 i.e 276/1423520 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1656/434, 6900/6560.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 1656/434,6900/6560
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 1656/434,6900/6560, numerators are 1656,6900
Denominators are 434,6560
The GCF of 1656,6900 is 276 .
LCM of 434,6560 is 1423520.
The greatest common factor of 1656/434,6900/6560 = [GCF of 1656,6900]/[LCM of 434,6560]= 276/1423520
Therefore, the GCF of 1656/434,6900/6560 is 276/1423520.
To find the highest common factor of 1656,6900, we have to find the factors of both numbers and list the highest common factor.
The factors of 1656 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 23, 24, 36, 46, 69, 72, 92, 138, 184, 207, 276, 414, 552, 828, 1656
The factors of 6900 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 23, 25, 30, 46, 50, 60, 69, 75, 92, 100, 115, 138, 150, 230, 276, 300, 345, 460, 575, 690, 1150, 1380, 1725, 2300, 3450, 6900
The HCF of 1656,6900 is 276.
Lets's calculate GCF of 1656,6900
2 | 1656, 6900 |
2 | 828, 3450 |
3 | 414, 1725 |
23 | 138, 575 |
6, 25 |
∴ So the GCF of the given numbers is 2 x 2 x 3 x 23 = 276
Now, list down the factors of 1656
:1,2,3,4,6,8,9,12,18,23,24,36,46,69,72,92,138,184,207,276,414,552,828,1656
Now, list down the factors of 6900
:1,2,3,4,5,6,10,12,15,20,23,25,30,46,50,60,69,75,92,100,115,138,150,230,276,300,345,460,575,690,1150,1380,1725,2300,3450,6900
Greatest Common Factor
We found the factors 1656,6900 . The biggest common factor number is the GCF number.
So the greatest common factor 1656,6900 is 276.
Lets's calculate LCM of 434,6560
2 | 434, 6560 |
217, 3280 |
∴ So the LCM of the given numbers is 2 x 217 x 3280 = 1423520
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 276/1423520
Therefore, the GCF of Fractions 1656/434,6900/6560 is 276/1423520
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 434,6560 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(434,6560) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(434,6560) x common factors =2 x 1 = 2
LCM(434,6560) = ( 434 × 6560 ) / 2
LCM(434,6560) = 2847040 / 2
LCM(434,6560) = 1423520
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 1656,6900?
The HCF of 1656,6900 is 276
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 1656/434, 6900/6560?
Answer: GCF of Numerators as per given numbers 1656/434, 6900/6560 is
GCF of Numerators i.e. for 1656,6900 is 276
LCM of denominators i.e. for 434,6560 is 1423520.
Thus, GCF of Fractions is 276/1423520.Finally, GCF of Fractions for 1656/434, 6900/6560 is 276/1423520.