GCF of 258/465, 360/762
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 258/465, 360/762 i.e 6/118110 easily. The following is the detailed procedure to determine the greatest common factor of fractions 258/465, 360/762.
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 258/465,360/762?
Given fractions are 258/465,360/762
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 258/465,360/762, numerators are 258,360
Denominators are 465,762
The GCF of 258,360 is 6 .
LCM of 465,762 is 118110.
The greatest common factor of 258/465,360/762 = [GCF of 258,360]/[LCM of 465,762]= 6/118110
Therefore, the GCF of 258/465,360/762 is 6/118110.
To find the highest common factor of 258,360, we have to find the factors of both numbers and list the highest common factor.
The factors of 258 are 1, 2, 3, 6, 43, 86, 129, 258
The factors of 360 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360
The HCF of 258,360 is 6.
Lets's calculate GCF of 258,360
| 2 | 258, 360 |
| 3 | 129, 180 |
| 43, 60 |
∴ So the GCF of the given numbers is 2 x 3 = 6
Greatest Common Factor of 258,360 By Matching Biggest Common Factor Method
Now, list down the factors of 258
:1,2,3,6,43,86,129,258
Now, list down the factors of 360
:1,2,3,4,5,6,8,9,10,12,15,18,20,24,30,36,40,45,60,72,90,120,180,360
Greatest Common Factor
We found the factors 258,360 . The biggest common factor number is the GCF number.
So the greatest common factor 258,360 is 6.
Lets's calculate LCM of 465,762
| 3 | 465, 762 |
| 155, 254 |
∴ So the LCM of the given numbers is 3 x 155 x 254 = 118110
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/118110
Therefore, the GCF of Fractions 258/465,360/762 is 6/118110
Least Common Multiple of 465,762 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 465,762 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(465,762) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(465,762) x common factors =3 x 1 = 3
LCM(465,762) = ( 465 × 762 ) / 3
LCM(465,762) = 354330 / 3
LCM(465,762) = 118110
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FAQs on GCF of Fractions of 258/465, 360/762
1. What is the HCF of 258,360?
The HCF of 258,360 is 6
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 258/465, 360/762?
Answer: GCF of Numerators as per given numbers 258/465, 360/762 is
GCF of Numerators i.e. for 258,360 is 6
LCM of denominators i.e. for 465,762 is 118110.
Thus, GCF of Fractions is 6/118110.Finally, GCF of Fractions for 258/465, 360/762 is 6/118110.