GCF of 8/58, 34/96, 32/416, 582/366
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 8/58, 34/96, 32/416, 582/366 i.e 2/2207712 easily. The following is the detailed procedure to determine the greatest common factor of fractions 8/58, 34/96, 32/416, 582/366.
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 8/58,34/96,32/416,582/366?
Given fractions are 8/58,34/96,32/416,582/366
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 8/58,34/96,32/416,582/366, numerators are 8,34,32,582
Denominators are 58,96,416,366
The GCF of 8,34,32,582 is 2 .
LCM of 58,96,416,366 is 2207712.
The greatest common factor of 8/58,34/96,32/416,582/366 = [GCF of 8,34,32,582]/[LCM of 58,96,416,366]= 2/2207712
Therefore, the GCF of 8/58,34/96,32/416,582/366 is 2/2207712.
To find the highest common factor of 8,34,32,582, we have to find the factors of both numbers and list the highest common factor.
The factors of 8 are 1, 2, 4, 8
The factors of 34 are 1, 2, 17, 34
The factors of 32 are 1, 2, 4, 8, 16, 32
The factors of 582 are 1, 2, 3, 6, 97, 194, 291, 582
The HCF of 8,34,32,582 is 2.
Lets's calculate GCF of 8,34,32,582
| 2 | 8, 34, 32, 582 |
| 4, 17, 16, 291 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 8,34,32,582 By Matching Biggest Common Factor Method
Now, list down the factors of 8
:1,2,4,8
Now, list down the factors of 34
:1,2,17,34
Now, list down the factors of 32
:1,2,4,8,16,32
Now, list down the factors of 582
:1,2,3,6,97,194,291,582
Greatest Common Factor
We found the factors 8,34,32,582 . The biggest common factor number is the GCF number.
So the greatest common factor 8,34,32,582 is 2.
Lets's calculate LCM of 58,96,416,366
| 2 | 58, 96, 416, 366 |
| 2 | 29, 48, 208, 183 |
| 2 | 29, 24, 104, 183 |
| 2 | 29, 12, 52, 183 |
| 2 | 29, 6, 26, 183 |
| 3 | 29, 3, 13, 183 |
| 29, 1, 13, 61 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 2 x 2 x 3 x 29 x 1 x 13 x 61 = 2207712
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/2207712
Therefore, the GCF of Fractions 8/58,34/96,32/416,582/366 is 2/2207712
Least Common Multiple of 58,96,416,366 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 58,96,416,366 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(58,96,416,366) = 2
common factors(in case of two or more numbers have common factors) = 192
GCF(58,96,416,366) x common factors =2 x 192 = 384
LCM(58,96,416,366) = ( 58 × 96 × 416 × 366 ) / 384
LCM(58,96,416,366) = 847761408 / 384
LCM(58,96,416,366) = 2207712
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FAQs on GCF of Fractions of 8/58, 34/96, 32/416, 582/366
1. What is the HCF of 8,34,32,582?
The HCF of 8,34,32,582 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 8/58, 34/96, 32/416, 582/366?
Answer: GCF of Numerators as per given numbers 8/58, 34/96, 32/416, 582/366 is
GCF of Numerators i.e. for 8,34,32,582 is 2
LCM of denominators i.e. for 58,96,416,366 is 2207712.
Thus, GCF of Fractions is 2/2207712.Finally, GCF of Fractions for 8/58, 34/96, 32/416, 582/366 is 2/2207712.