GCF of 224/205, 560/498
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 224/205, 560/498 i.e 112/102090 easily. The following is the detailed procedure to determine the greatest common factor of fractions 224/205, 560/498.
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 224/205,560/498?
Given fractions are 224/205,560/498
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 224/205,560/498, numerators are 224,560
Denominators are 205,498
The GCF of 224,560 is 112 .
LCM of 205,498 is 102090.
The greatest common factor of 224/205,560/498 = [GCF of 224,560]/[LCM of 205,498]= 112/102090
Therefore, the GCF of 224/205,560/498 is 112/102090.
To find the highest common factor of 224,560, we have to find the factors of both numbers and list the highest common factor.
The factors of 224 are 1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 112, 224
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 HCF of 224,560 is 112.
Lets's calculate GCF of 224,560
| 2 | 224, 560 |
| 2 | 112, 280 |
| 2 | 56, 140 |
| 2 | 28, 70 |
| 7 | 14, 35 |
| 2, 5 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 2 x 7 = 112
Greatest Common Factor of 224,560 By Matching Biggest Common Factor Method
Now, list down the factors of 224
:1,2,4,7,8,14,16,28,32,56,112,224
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
Greatest Common Factor
We found the factors 224,560 . The biggest common factor number is the GCF number.
So the greatest common factor 224,560 is 112.
Lets's calculate LCM of 205,498
Given numbers has no common factors except 1. So, there LCM is their product i.e 102090
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 112/102090
Therefore, the GCF of Fractions 224/205,560/498 is 112/102090
Least Common Multiple of 205,498 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 205,498 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(205,498) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(205,498) x common factors =1 x 1 = 1
LCM(205,498) = ( 205 × 498 ) / 1
LCM(205,498) = 102090 / 1
LCM(205,498) = 102090
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FAQs on GCF of Fractions of 224/205, 560/498
1. What is the HCF of 224,560?
The HCF of 224,560 is 112
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 224/205, 560/498?
Answer: GCF of Numerators as per given numbers 224/205, 560/498 is
GCF of Numerators i.e. for 224,560 is 112
LCM of denominators i.e. for 205,498 is 102090.
Thus, GCF of Fractions is 112/102090.Finally, GCF of Fractions for 224/205, 560/498 is 112/102090.