GCF of 5730/320, 8300/158
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 5730/320, 8300/158 i.e 10/25280 easily. The following is the detailed procedure to determine the greatest common factor of fractions 5730/320, 8300/158.
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 5730/320,8300/158?
Given fractions are 5730/320,8300/158
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 5730/320,8300/158, numerators are 5730,8300
Denominators are 320,158
The GCF of 5730,8300 is 10 .
LCM of 320,158 is 25280.
The greatest common factor of 5730/320,8300/158 = [GCF of 5730,8300]/[LCM of 320,158]= 10/25280
Therefore, the GCF of 5730/320,8300/158 is 10/25280.
To find the highest common factor of 5730,8300, we have to find the factors of both numbers and list the highest common factor.
The factors of 5730 are 1, 2, 3, 5, 6, 10, 15, 30, 191, 382, 573, 955, 1146, 1910, 2865, 5730
The factors of 8300 are 1, 2, 4, 5, 10, 20, 25, 50, 83, 100, 166, 332, 415, 830, 1660, 2075, 4150, 8300
The HCF of 5730,8300 is 10.
Lets's calculate GCF of 5730,8300
| 2 | 5730, 8300 |
| 5 | 2865, 4150 |
| 573, 830 |
∴ So the GCF of the given numbers is 2 x 5 = 10
Greatest Common Factor of 5730,8300 By Matching Biggest Common Factor Method
Now, list down the factors of 5730
:1,2,3,5,6,10,15,30,191,382,573,955,1146,1910,2865,5730
Now, list down the factors of 8300
:1,2,4,5,10,20,25,50,83,100,166,332,415,830,1660,2075,4150,8300
Greatest Common Factor
We found the factors 5730,8300 . The biggest common factor number is the GCF number.
So the greatest common factor 5730,8300 is 10.
Lets's calculate LCM of 320,158
| 2 | 320, 158 |
| 160, 79 |
∴ So the LCM of the given numbers is 2 x 160 x 79 = 25280
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 10/25280
Therefore, the GCF of Fractions 5730/320,8300/158 is 10/25280
Least Common Multiple of 320,158 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 320,158 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(320,158) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(320,158) x common factors =2 x 1 = 2
LCM(320,158) = ( 320 × 158 ) / 2
LCM(320,158) = 50560 / 2
LCM(320,158) = 25280
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FAQs on GCF of Fractions of 5730/320, 8300/158
1. What is the HCF of 5730,8300?
The HCF of 5730,8300 is 10
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 5730/320, 8300/158?
Answer: GCF of Numerators as per given numbers 5730/320, 8300/158 is
GCF of Numerators i.e. for 5730,8300 is 10
LCM of denominators i.e. for 320,158 is 25280.
Thus, GCF of Fractions is 10/25280.Finally, GCF of Fractions for 5730/320, 8300/158 is 10/25280.