Use our free GCF of Fractions Calculator tool to compute the GCF of 160/676, 360/714 i.e 40/241332 easily. The following is the detailed procedure to determine the greatest common factor of fractions 160/676, 360/714.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 160/676,360/714
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 160/676,360/714, numerators are 160,360
Denominators are 676,714
The GCF of 160,360 is 40 .
LCM of 676,714 is 241332.
The greatest common factor of 160/676,360/714 = [GCF of 160,360]/[LCM of 676,714]= 40/241332
Therefore, the GCF of 160/676,360/714 is 40/241332.
To find the highest common factor of 160,360, we have to find the factors of both numbers and list the highest common factor.
The factors of 160 are 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 80, 160
The factors of 360 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360
The HCF of 160,360 is 40.
Lets's calculate GCF of 160,360
2 | 160, 360 |
2 | 80, 180 |
2 | 40, 90 |
5 | 20, 45 |
4, 9 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 5 = 40
Now, list down the factors of 160
:1,2,4,5,8,10,16,20,32,40,80,160
Now, list down the factors of 360
:1,2,3,4,5,6,8,9,10,12,15,18,20,24,30,36,40,45,60,72,90,120,180,360
Greatest Common Factor
We found the factors 160,360 . The biggest common factor number is the GCF number.
So the greatest common factor 160,360 is 40.
Lets's calculate LCM of 676,714
2 | 676, 714 |
338, 357 |
∴ So the LCM of the given numbers is 2 x 338 x 357 = 241332
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 40/241332
Therefore, the GCF of Fractions 160/676,360/714 is 40/241332
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 676,714 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(676,714) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(676,714) x common factors =2 x 1 = 2
LCM(676,714) = ( 676 × 714 ) / 2
LCM(676,714) = 482664 / 2
LCM(676,714) = 241332
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 160,360?
The HCF of 160,360 is 40
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 160/676, 360/714?
Answer: GCF of Numerators as per given numbers 160/676, 360/714 is
GCF of Numerators i.e. for 160,360 is 40
LCM of denominators i.e. for 676,714 is 241332.
Thus, GCF of Fractions is 40/241332.Finally, GCF of Fractions for 160/676, 360/714 is 40/241332.