GCF of 360/654, 190/229, 340/419
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 360/654, 190/229, 340/419 i.e 10/62751954 easily. The following is the detailed procedure to determine the greatest common factor of fractions 360/654, 190/229, 340/419.
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 360/654,190/229,340/419?
Given fractions are 360/654,190/229,340/419
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 360/654,190/229,340/419, numerators are 360,190,340
Denominators are 654,229,419
The GCF of 360,190,340 is 10 .
LCM of 654,229,419 is 62751954.
The greatest common factor of 360/654,190/229,340/419 = [GCF of 360,190,340]/[LCM of 654,229,419]= 10/62751954
Therefore, the GCF of 360/654,190/229,340/419 is 10/62751954.
To find the highest common factor of 360,190,340, 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 190 are 1, 2, 5, 10, 19, 38, 95, 190
The factors of 340 are 1, 2, 4, 5, 10, 17, 20, 34, 68, 85, 170, 340
The HCF of 360,190,340 is 10.
Lets's calculate GCF of 360,190,340
| 2 | 360, 190, 340 |
| 5 | 180, 95, 170 |
| 36, 19, 34 |
∴ So the GCF of the given numbers is 2 x 5 = 10
Greatest Common Factor of 360,190,340 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 190
:1,2,5,10,19,38,95,190
Now, list down the factors of 340
:1,2,4,5,10,17,20,34,68,85,170,340
Greatest Common Factor
We found the factors 360,190,340 . The biggest common factor number is the GCF number.
So the greatest common factor 360,190,340 is 10.
Lets's calculate LCM of 654,229,419
Given numbers has no common factors except 1. So, there LCM is their product i.e 62751954
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 10/62751954
Therefore, the GCF of Fractions 360/654,190/229,340/419 is 10/62751954
Least Common Multiple of 654,229,419 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 654,229,419 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(654,229,419) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(654,229,419) x common factors =1 x 1 = 1
LCM(654,229,419) = ( 654 × 229 × 419 ) / 1
LCM(654,229,419) = 62751954 / 1
LCM(654,229,419) = 62751954
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FAQs on GCF of Fractions of 360/654, 190/229, 340/419
1. What is the HCF of 360,190,340?
The HCF of 360,190,340 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 360/654, 190/229, 340/419?
Answer: GCF of Numerators as per given numbers 360/654, 190/229, 340/419 is
GCF of Numerators i.e. for 360,190,340 is 10
LCM of denominators i.e. for 654,229,419 is 62751954.
Thus, GCF of Fractions is 10/62751954.Finally, GCF of Fractions for 360/654, 190/229, 340/419 is 10/62751954.