GCF of 435/20, 144/560
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 435/20, 144/560 i.e 3/560 easily. The following is the detailed procedure to determine the greatest common factor of fractions 435/20, 144/560.
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 435/20,144/560?
Given fractions are 435/20,144/560
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 435/20,144/560, numerators are 435,144
Denominators are 20,560
The GCF of 435,144 is 3 .
LCM of 20,560 is 560.
The greatest common factor of 435/20,144/560 = [GCF of 435,144]/[LCM of 20,560]= 3/560
Therefore, the GCF of 435/20,144/560 is 3/560.
To find the highest common factor of 435,144, we have to find the factors of both numbers and list the highest common factor.
The factors of 435 are 1, 3, 5, 15, 29, 87, 145, 435
The factors of 144 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144
The HCF of 435,144 is 3.
Lets's calculate GCF of 435,144
| 3 | 435, 144 |
| 145, 48 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 435,144 By Matching Biggest Common Factor Method
Now, list down the factors of 435
:1,3,5,15,29,87,145,435
Now, list down the factors of 144
:1,2,3,4,6,8,9,12,16,18,24,36,48,72,144
Greatest Common Factor
We found the factors 435,144 . The biggest common factor number is the GCF number.
So the greatest common factor 435,144 is 3.
Lets's calculate LCM of 20,560
| 2 | 20, 560 |
| 2 | 10, 280 |
| 5 | 5, 140 |
| 1, 28 |
∴ So the LCM of the given numbers is 2 x 2 x 5 x 1 x 28 = 560
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/560
Therefore, the GCF of Fractions 435/20,144/560 is 3/560
Least Common Multiple of 20,560 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 20,560 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(20,560) = 20
common factors(in case of two or more numbers have common factors) = 1
GCF(20,560) x common factors =20 x 1 = 20
LCM(20,560) = ( 20 × 560 ) / 20
LCM(20,560) = 11200 / 20
LCM(20,560) = 560
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FAQs on GCF of Fractions of 435/20, 144/560
1. What is the HCF of 435,144?
The HCF of 435,144 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 435/20, 144/560?
Answer: GCF of Numerators as per given numbers 435/20, 144/560 is
GCF of Numerators i.e. for 435,144 is 3
LCM of denominators i.e. for 20,560 is 560.
Thus, GCF of Fractions is 3/560.Finally, GCF of Fractions for 435/20, 144/560 is 3/560.