GCF of 282/27, 320/763
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 282/27, 320/763 i.e 2/20601 easily. The following is the detailed procedure to determine the greatest common factor of fractions 282/27, 320/763.
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 282/27,320/763?
Given fractions are 282/27,320/763
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 282/27,320/763, numerators are 282,320
Denominators are 27,763
The GCF of 282,320 is 2 .
LCM of 27,763 is 20601.
The greatest common factor of 282/27,320/763 = [GCF of 282,320]/[LCM of 27,763]= 2/20601
Therefore, the GCF of 282/27,320/763 is 2/20601.
To find the highest common factor of 282,320, we have to find the factors of both numbers and list the highest common factor.
The factors of 282 are 1, 2, 3, 6, 47, 94, 141, 282
The factors of 320 are 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 80, 160, 320
The HCF of 282,320 is 2.
Lets's calculate GCF of 282,320
| 2 | 282, 320 |
| 141, 160 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 282,320 By Matching Biggest Common Factor Method
Now, list down the factors of 282
:1,2,3,6,47,94,141,282
Now, list down the factors of 320
:1,2,4,5,8,10,16,20,32,40,64,80,160,320
Greatest Common Factor
We found the factors 282,320 . The biggest common factor number is the GCF number.
So the greatest common factor 282,320 is 2.
Lets's calculate LCM of 27,763
Given numbers has no common factors except 1. So, there LCM is their product i.e 20601
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/20601
Therefore, the GCF of Fractions 282/27,320/763 is 2/20601
Least Common Multiple of 27,763 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 27,763 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(27,763) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(27,763) x common factors =1 x 1 = 1
LCM(27,763) = ( 27 × 763 ) / 1
LCM(27,763) = 20601 / 1
LCM(27,763) = 20601
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FAQs on GCF of Fractions of 282/27, 320/763
1. What is the HCF of 282,320?
The HCF of 282,320 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 282/27, 320/763?
Answer: GCF of Numerators as per given numbers 282/27, 320/763 is
GCF of Numerators i.e. for 282,320 is 2
LCM of denominators i.e. for 27,763 is 20601.
Thus, GCF of Fractions is 2/20601.Finally, GCF of Fractions for 282/27, 320/763 is 2/20601.