GCF of 930/258, 960/413
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 930/258, 960/413 i.e 30/106554 easily. The following is the detailed procedure to determine the greatest common factor of fractions 930/258, 960/413.
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 930/258,960/413?
Given fractions are 930/258,960/413
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 930/258,960/413, numerators are 930,960
Denominators are 258,413
The GCF of 930,960 is 30 .
LCM of 258,413 is 106554.
The greatest common factor of 930/258,960/413 = [GCF of 930,960]/[LCM of 258,413]= 30/106554
Therefore, the GCF of 930/258,960/413 is 30/106554.
To find the highest common factor of 930,960, we have to find the factors of both numbers and list the highest common factor.
The factors of 930 are 1, 2, 3, 5, 6, 10, 15, 30, 31, 62, 93, 155, 186, 310, 465, 930
The factors of 960 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 64, 80, 96, 120, 160, 192, 240, 320, 480, 960
The HCF of 930,960 is 30.
Lets's calculate GCF of 930,960
| 2 | 930, 960 |
| 3 | 465, 480 |
| 5 | 155, 160 |
| 31, 32 |
∴ So the GCF of the given numbers is 2 x 3 x 5 = 30
Greatest Common Factor of 930,960 By Matching Biggest Common Factor Method
Now, list down the factors of 930
:1,2,3,5,6,10,15,30,31,62,93,155,186,310,465,930
Now, list down the factors of 960
:1,2,3,4,5,6,8,10,12,15,16,20,24,30,32,40,48,60,64,80,96,120,160,192,240,320,480,960
Greatest Common Factor
We found the factors 930,960 . The biggest common factor number is the GCF number.
So the greatest common factor 930,960 is 30.
Lets's calculate LCM of 258,413
Given numbers has no common factors except 1. So, there LCM is their product i.e 106554
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 30/106554
Therefore, the GCF of Fractions 930/258,960/413 is 30/106554
Least Common Multiple of 258,413 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 258,413 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(258,413) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(258,413) x common factors =1 x 1 = 1
LCM(258,413) = ( 258 × 413 ) / 1
LCM(258,413) = 106554 / 1
LCM(258,413) = 106554
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FAQs on GCF of Fractions of 930/258, 960/413
1. What is the HCF of 930,960?
The HCF of 930,960 is 30
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 930/258, 960/413?
Answer: GCF of Numerators as per given numbers 930/258, 960/413 is
GCF of Numerators i.e. for 930,960 is 30
LCM of denominators i.e. for 258,413 is 106554.
Thus, GCF of Fractions is 30/106554.Finally, GCF of Fractions for 930/258, 960/413 is 30/106554.