GCF of 282/66, 420/83, 766/89
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 282/66, 420/83, 766/89 i.e 2/487542 easily. The following is the detailed procedure to determine the greatest common factor of fractions 282/66, 420/83, 766/89.
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 282/66,420/83,766/89?
Given fractions are 282/66,420/83,766/89
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 282/66,420/83,766/89, numerators are 282,420,766
Denominators are 66,83,89
The GCF of 282,420,766 is 2 .
LCM of 66,83,89 is 487542.
The greatest common factor of 282/66,420/83,766/89 = [GCF of 282,420,766]/[LCM of 66,83,89]= 2/487542
Therefore, the GCF of 282/66,420/83,766/89 is 2/487542.
To find the highest common factor of 282,420,766, 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 420 are 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, 420
The factors of 766 are 1, 2, 383, 766
The HCF of 282,420,766 is 2.
Lets's calculate GCF of 282,420,766
| 2 | 282, 420, 766 |
| 141, 210, 383 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 282,420,766 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 420
:1,2,3,4,5,6,7,10,12,14,15,20,21,28,30,35,42,60,70,84,105,140,210,420
Now, list down the factors of 766
:1,2,383,766
Greatest Common Factor
We found the factors 282,420,766 . The biggest common factor number is the GCF number.
So the greatest common factor 282,420,766 is 2.
Lets's calculate LCM of 66,83,89
Given numbers has no common factors except 1. So, there LCM is their product i.e 487542
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/487542
Therefore, the GCF of Fractions 282/66,420/83,766/89 is 2/487542
Least Common Multiple of 66,83,89 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 66,83,89 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(66,83,89) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(66,83,89) x common factors =1 x 1 = 1
LCM(66,83,89) = ( 66 × 83 × 89 ) / 1
LCM(66,83,89) = 487542 / 1
LCM(66,83,89) = 487542
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FAQs on GCF of Fractions of 282/66, 420/83, 766/89
1. What is the HCF of 282,420,766?
The HCF of 282,420,766 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 282/66, 420/83, 766/89?
Answer: GCF of Numerators as per given numbers 282/66, 420/83, 766/89 is
GCF of Numerators i.e. for 282,420,766 is 2
LCM of denominators i.e. for 66,83,89 is 487542.
Thus, GCF of Fractions is 2/487542.Finally, GCF of Fractions for 282/66, 420/83, 766/89 is 2/487542.