GCF of 442/106, 512/241
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 442/106, 512/241 i.e 2/25546 easily. The following is the detailed procedure to determine the greatest common factor of fractions 442/106, 512/241.
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 442/106,512/241?
Given fractions are 442/106,512/241
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 442/106,512/241, numerators are 442,512
Denominators are 106,241
The GCF of 442,512 is 2 .
LCM of 106,241 is 25546.
The greatest common factor of 442/106,512/241 = [GCF of 442,512]/[LCM of 106,241]= 2/25546
Therefore, the GCF of 442/106,512/241 is 2/25546.
To find the highest common factor of 442,512, we have to find the factors of both numbers and list the highest common factor.
The factors of 442 are 1, 2, 13, 17, 26, 34, 221, 442
The factors of 512 are 1, 2, 4, 8, 16, 32, 64, 128, 256, 512
The HCF of 442,512 is 2.
Lets's calculate GCF of 442,512
| 2 | 442, 512 |
| 221, 256 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 442,512 By Matching Biggest Common Factor Method
Now, list down the factors of 442
:1,2,13,17,26,34,221,442
Now, list down the factors of 512
:1,2,4,8,16,32,64,128,256,512
Greatest Common Factor
We found the factors 442,512 . The biggest common factor number is the GCF number.
So the greatest common factor 442,512 is 2.
Lets's calculate LCM of 106,241
Given numbers has no common factors except 1. So, there LCM is their product i.e 25546
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/25546
Therefore, the GCF of Fractions 442/106,512/241 is 2/25546
Least Common Multiple of 106,241 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 106,241 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(106,241) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(106,241) x common factors =1 x 1 = 1
LCM(106,241) = ( 106 × 241 ) / 1
LCM(106,241) = 25546 / 1
LCM(106,241) = 25546
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FAQs on GCF of Fractions of 442/106, 512/241
1. What is the HCF of 442,512?
The HCF of 442,512 is 2
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 442/106, 512/241?
Answer: GCF of Numerators as per given numbers 442/106, 512/241 is
GCF of Numerators i.e. for 442,512 is 2
LCM of denominators i.e. for 106,241 is 25546.
Thus, GCF of Fractions is 2/25546.Finally, GCF of Fractions for 442/106, 512/241 is 2/25546.