GCF of 71/21, 378/59, 489/966
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 71/21, 378/59, 489/966 i.e 1/56994 easily. The following is the detailed procedure to determine the greatest common factor of fractions 71/21, 378/59, 489/966.
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 71/21,378/59,489/966?
Given fractions are 71/21,378/59,489/966
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 71/21,378/59,489/966, numerators are 71,378,489
Denominators are 21,59,966
The GCF of 71,378,489 is 1 .
LCM of 21,59,966 is 56994.
The greatest common factor of 71/21,378/59,489/966 = [GCF of 71,378,489]/[LCM of 21,59,966]= 1/56994
Therefore, the GCF of 71/21,378/59,489/966 is 1/56994.
To find the highest common factor of 71,378,489, we have to find the factors of both numbers and list the highest common factor.
The factors of 71 are 1, 71
The factors of 378 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 27, 42, 54, 63, 126, 189, 378
The factors of 489 are 1, 3, 163, 489
The HCF of 71,378,489 is 1.
Lets's calculate GCF of 71,378,489
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 71,378,489 By Matching Biggest Common Factor Method
Now, list down the factors of 71
:1,71
Now, list down the factors of 378
:1,2,3,6,7,9,14,18,21,27,42,54,63,126,189,378
Now, list down the factors of 489
:1,3,163,489
Greatest Common Factor
We found the factors 71,378,489 . The biggest common factor number is the GCF number.
So the greatest common factor 71,378,489 is 1.
Lets's calculate LCM of 21,59,966
| 3 | 21, 59, 966 |
| 7 | 7, 59, 322 |
| 1, 59, 46 |
∴ So the LCM of the given numbers is 3 x 7 x 1 x 59 x 46 = 56994
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/56994
Therefore, the GCF of Fractions 71/21,378/59,489/966 is 1/56994
Least Common Multiple of 21,59,966 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 21,59,966 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(21,59,966) = 1
common factors(in case of two or more numbers have common factors) = 21
GCF(21,59,966) x common factors =1 x 21 = 21
LCM(21,59,966) = ( 21 × 59 × 966 ) / 21
LCM(21,59,966) = 1196874 / 21
LCM(21,59,966) = 56994
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FAQs on GCF of Fractions of 71/21, 378/59, 489/966
1. What is the HCF of 71,378,489?
The HCF of 71,378,489 is 1
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 71/21, 378/59, 489/966?
Answer: GCF of Numerators as per given numbers 71/21, 378/59, 489/966 is
GCF of Numerators i.e. for 71,378,489 is 1
LCM of denominators i.e. for 21,59,966 is 56994.
Thus, GCF of Fractions is 1/56994.Finally, GCF of Fractions for 71/21, 378/59, 489/966 is 1/56994.