GCF of 816/65, 708/35, 584/65
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 816/65, 708/35, 584/65 i.e 4/455 easily. The following is the detailed procedure to determine the greatest common factor of fractions 816/65, 708/35, 584/65.
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 816/65,708/35,584/65?
Given fractions are 816/65,708/35,584/65
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 816/65,708/35,584/65, numerators are 816,708,584
Denominators are 65,35,65
The GCF of 816,708,584 is 4 .
LCM of 65,35,65 is 455.
The greatest common factor of 816/65,708/35,584/65 = [GCF of 816,708,584]/[LCM of 65,35,65]= 4/455
Therefore, the GCF of 816/65,708/35,584/65 is 4/455.
To find the highest common factor of 816,708,584, we have to find the factors of both numbers and list the highest common factor.
The factors of 816 are 1, 2, 3, 4, 6, 8, 12, 16, 17, 24, 34, 48, 51, 68, 102, 136, 204, 272, 408, 816
The factors of 708 are 1, 2, 3, 4, 6, 12, 59, 118, 177, 236, 354, 708
The factors of 584 are 1, 2, 4, 8, 73, 146, 292, 584
The HCF of 816,708,584 is 4.
Lets's calculate GCF of 816,708,584
| 2 | 816, 708, 584 |
| 2 | 408, 354, 292 |
| 204, 177, 146 |
∴ So the GCF of the given numbers is 2 x 2 = 4
Greatest Common Factor of 816,708,584 By Matching Biggest Common Factor Method
Now, list down the factors of 816
:1,2,3,4,6,8,12,16,17,24,34,48,51,68,102,136,204,272,408,816
Now, list down the factors of 708
:1,2,3,4,6,12,59,118,177,236,354,708
Now, list down the factors of 584
:1,2,4,8,73,146,292,584
Greatest Common Factor
We found the factors 816,708,584 . The biggest common factor number is the GCF number.
So the greatest common factor 816,708,584 is 4.
Lets's calculate LCM of 65,35,65
| 5 | 65, 35, 65 |
| 13 | 13, 7, 13 |
| 1, 7, 1 |
∴ So the LCM of the given numbers is 5 x 13 x 1 x 7 x 1 = 455
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/455
Therefore, the GCF of Fractions 816/65,708/35,584/65 is 4/455
Least Common Multiple of 65,35,65 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 65,35,65 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(65,35,65) = 5
common factors(in case of two or more numbers have common factors) = 65
GCF(65,35,65) x common factors =5 x 65 = 325
LCM(65,35,65) = ( 65 × 35 × 65 ) / 325
LCM(65,35,65) = 147875 / 325
LCM(65,35,65) = 455
GCF of Fractions Calculation Examples
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FAQs on GCF of Fractions of 816/65, 708/35, 584/65
1. What is the HCF of 816,708,584?
The HCF of 816,708,584 is 4
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 816/65, 708/35, 584/65?
Answer: GCF of Numerators as per given numbers 816/65, 708/35, 584/65 is
GCF of Numerators i.e. for 816,708,584 is 4
LCM of denominators i.e. for 65,35,65 is 455.
Thus, GCF of Fractions is 4/455.Finally, GCF of Fractions for 816/65, 708/35, 584/65 is 4/455.