GCF of 760/91, 840/86, 984/91
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 760/91, 840/86, 984/91 i.e 8/7826 easily. The following is the detailed procedure to determine the greatest common factor of fractions 760/91, 840/86, 984/91.
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 760/91,840/86,984/91?
Given fractions are 760/91,840/86,984/91
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 760/91,840/86,984/91, numerators are 760,840,984
Denominators are 91,86,91
The GCF of 760,840,984 is 8 .
LCM of 91,86,91 is 7826.
The greatest common factor of 760/91,840/86,984/91 = [GCF of 760,840,984]/[LCM of 91,86,91]= 8/7826
Therefore, the GCF of 760/91,840/86,984/91 is 8/7826.
To find the highest common factor of 760,840,984, we have to find the factors of both numbers and list the highest common factor.
The factors of 760 are 1, 2, 4, 5, 8, 10, 19, 20, 38, 40, 76, 95, 152, 190, 380, 760
The factors of 840 are 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24, 28, 30, 35, 40, 42, 56, 60, 70, 84, 105, 120, 140, 168, 210, 280, 420, 840
The factors of 984 are 1, 2, 3, 4, 6, 8, 12, 24, 41, 82, 123, 164, 246, 328, 492, 984
The HCF of 760,840,984 is 8.
Lets's calculate GCF of 760,840,984
| 2 | 760, 840, 984 |
| 2 | 380, 420, 492 |
| 2 | 190, 210, 246 |
| 95, 105, 123 |
∴ So the GCF of the given numbers is 2 x 2 x 2 = 8
Greatest Common Factor of 760,840,984 By Matching Biggest Common Factor Method
Now, list down the factors of 760
:1,2,4,5,8,10,19,20,38,40,76,95,152,190,380,760
Now, list down the factors of 840
:1,2,3,4,5,6,7,8,10,12,14,15,20,21,24,28,30,35,40,42,56,60,70,84,105,120,140,168,210,280,420,840
Now, list down the factors of 984
:1,2,3,4,6,8,12,24,41,82,123,164,246,328,492,984
Greatest Common Factor
We found the factors 760,840,984 . The biggest common factor number is the GCF number.
So the greatest common factor 760,840,984 is 8.
Lets's calculate LCM of 91,86,91
| 7 | 91, 86, 91 |
| 13 | 13, 86, 13 |
| 1, 86, 1 |
∴ So the LCM of the given numbers is 7 x 13 x 1 x 86 x 1 = 7826
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 8/7826
Therefore, the GCF of Fractions 760/91,840/86,984/91 is 8/7826
Least Common Multiple of 91,86,91 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 91,86,91 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(91,86,91) = 1
common factors(in case of two or more numbers have common factors) = 91
GCF(91,86,91) x common factors =1 x 91 = 91
LCM(91,86,91) = ( 91 × 86 × 91 ) / 91
LCM(91,86,91) = 712166 / 91
LCM(91,86,91) = 7826
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FAQs on GCF of Fractions of 760/91, 840/86, 984/91
1. What is the HCF of 760,840,984?
The HCF of 760,840,984 is 8
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 760/91, 840/86, 984/91?
Answer: GCF of Numerators as per given numbers 760/91, 840/86, 984/91 is
GCF of Numerators i.e. for 760,840,984 is 8
LCM of denominators i.e. for 91,86,91 is 7826.
Thus, GCF of Fractions is 8/7826.Finally, GCF of Fractions for 760/91, 840/86, 984/91 is 8/7826.