GCF of 198/460, 705/560
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 198/460, 705/560 i.e 3/12880 easily. The following is the detailed procedure to determine the greatest common factor of fractions 198/460, 705/560.
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 198/460,705/560?
Given fractions are 198/460,705/560
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 198/460,705/560, numerators are 198,705
Denominators are 460,560
The GCF of 198,705 is 3 .
LCM of 460,560 is 12880.
The greatest common factor of 198/460,705/560 = [GCF of 198,705]/[LCM of 460,560]= 3/12880
Therefore, the GCF of 198/460,705/560 is 3/12880.
To find the highest common factor of 198,705, we have to find the factors of both numbers and list the highest common factor.
The factors of 198 are 1, 2, 3, 6, 9, 11, 18, 22, 33, 66, 99, 198
The factors of 705 are 1, 3, 5, 15, 47, 141, 235, 705
The HCF of 198,705 is 3.
Lets's calculate GCF of 198,705
| 3 | 198, 705 |
| 66, 235 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 198,705 By Matching Biggest Common Factor Method
Now, list down the factors of 198
:1,2,3,6,9,11,18,22,33,66,99,198
Now, list down the factors of 705
:1,3,5,15,47,141,235,705
Greatest Common Factor
We found the factors 198,705 . The biggest common factor number is the GCF number.
So the greatest common factor 198,705 is 3.
Lets's calculate LCM of 460,560
| 2 | 460, 560 |
| 2 | 230, 280 |
| 5 | 115, 140 |
| 23, 28 |
∴ So the LCM of the given numbers is 2 x 2 x 5 x 23 x 28 = 12880
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/12880
Therefore, the GCF of Fractions 198/460,705/560 is 3/12880
Least Common Multiple of 460,560 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 460,560 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(460,560) = 20
common factors(in case of two or more numbers have common factors) = 1
GCF(460,560) x common factors =20 x 1 = 20
LCM(460,560) = ( 460 × 560 ) / 20
LCM(460,560) = 257600 / 20
LCM(460,560) = 12880
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FAQs on GCF of Fractions of 198/460, 705/560
1. What is the HCF of 198,705?
The HCF of 198,705 is 3
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 198/460, 705/560?
Answer: GCF of Numerators as per given numbers 198/460, 705/560 is
GCF of Numerators i.e. for 198,705 is 3
LCM of denominators i.e. for 460,560 is 12880.
Thus, GCF of Fractions is 3/12880.Finally, GCF of Fractions for 198/460, 705/560 is 3/12880.