GCF of 360/119, 1230/1386
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 360/119, 1230/1386 i.e 30/23562 easily. The following is the detailed procedure to determine the greatest common factor of fractions 360/119, 1230/1386.
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 360/119,1230/1386?
Given fractions are 360/119,1230/1386
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 360/119,1230/1386, numerators are 360,1230
Denominators are 119,1386
The GCF of 360,1230 is 30 .
LCM of 119,1386 is 23562.
The greatest common factor of 360/119,1230/1386 = [GCF of 360,1230]/[LCM of 119,1386]= 30/23562
Therefore, the GCF of 360/119,1230/1386 is 30/23562.
To find the highest common factor of 360,1230, we have to find the factors of both numbers and list the highest common factor.
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 factors of 1230 are 1, 2, 3, 5, 6, 10, 15, 30, 41, 82, 123, 205, 246, 410, 615, 1230
The HCF of 360,1230 is 30.
Lets's calculate GCF of 360,1230
| 2 | 360, 1230 |
| 3 | 180, 615 |
| 5 | 60, 205 |
| 12, 41 |
∴ So the GCF of the given numbers is 2 x 3 x 5 = 30
Greatest Common Factor of 360,1230 By Matching Biggest Common Factor Method
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
Now, list down the factors of 1230
:1,2,3,5,6,10,15,30,41,82,123,205,246,410,615,1230
Greatest Common Factor
We found the factors 360,1230 . The biggest common factor number is the GCF number.
So the greatest common factor 360,1230 is 30.
Lets's calculate LCM of 119,1386
| 7 | 119, 1386 |
| 17, 198 |
∴ So the LCM of the given numbers is 7 x 17 x 198 = 23562
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 30/23562
Therefore, the GCF of Fractions 360/119,1230/1386 is 30/23562
Least Common Multiple of 119,1386 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 119,1386 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(119,1386) = 7
common factors(in case of two or more numbers have common factors) = 1
GCF(119,1386) x common factors =7 x 1 = 7
LCM(119,1386) = ( 119 × 1386 ) / 7
LCM(119,1386) = 164934 / 7
LCM(119,1386) = 23562
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FAQs on GCF of Fractions of 360/119, 1230/1386
1. What is the HCF of 360,1230?
The HCF of 360,1230 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 360/119, 1230/1386?
Answer: GCF of Numerators as per given numbers 360/119, 1230/1386 is
GCF of Numerators i.e. for 360,1230 is 30
LCM of denominators i.e. for 119,1386 is 23562.
Thus, GCF of Fractions is 30/23562.Finally, GCF of Fractions for 360/119, 1230/1386 is 30/23562.