GCF of 30/680, 75/622, 216/219
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 30/680, 75/622, 216/219 i.e 3/46314120 easily. The following is the detailed procedure to determine the greatest common factor of fractions 30/680, 75/622, 216/219.
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 30/680,75/622,216/219?
Given fractions are 30/680,75/622,216/219
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 30/680,75/622,216/219, numerators are 30,75,216
Denominators are 680,622,219
The GCF of 30,75,216 is 3 .
LCM of 680,622,219 is 46314120.
The greatest common factor of 30/680,75/622,216/219 = [GCF of 30,75,216]/[LCM of 680,622,219]= 3/46314120
Therefore, the GCF of 30/680,75/622,216/219 is 3/46314120.
To find the highest common factor of 30,75,216, we have to find the factors of both numbers and list the highest common factor.
The factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30
The factors of 75 are 1, 3, 5, 15, 25, 75
The factors of 216 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, 216
The HCF of 30,75,216 is 3.
Lets's calculate GCF of 30,75,216
| 3 | 30, 75, 216 |
| 10, 25, 72 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 30,75,216 By Matching Biggest Common Factor Method
Now, list down the factors of 30
:1,2,3,5,6,10,15,30
Now, list down the factors of 75
:1,3,5,15,25,75
Now, list down the factors of 216
:1,2,3,4,6,8,9,12,18,24,27,36,54,72,108,216
Greatest Common Factor
We found the factors 30,75,216 . The biggest common factor number is the GCF number.
So the greatest common factor 30,75,216 is 3.
Lets's calculate LCM of 680,622,219
| 2 | 680, 622, 219 |
| 340, 311, 219 |
∴ So the LCM of the given numbers is 2 x 340 x 311 x 219 = 46314120
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/46314120
Therefore, the GCF of Fractions 30/680,75/622,216/219 is 3/46314120
Least Common Multiple of 680,622,219 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 680,622,219 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(680,622,219) = 1
common factors(in case of two or more numbers have common factors) = 2
GCF(680,622,219) x common factors =1 x 2 = 2
LCM(680,622,219) = ( 680 × 622 × 219 ) / 2
LCM(680,622,219) = 92628240 / 2
LCM(680,622,219) = 46314120
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FAQs on GCF of Fractions of 30/680, 75/622, 216/219
1. What is the HCF of 30,75,216?
The HCF of 30,75,216 is 3
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 30/680, 75/622, 216/219?
Answer: GCF of Numerators as per given numbers 30/680, 75/622, 216/219 is
GCF of Numerators i.e. for 30,75,216 is 3
LCM of denominators i.e. for 680,622,219 is 46314120.
Thus, GCF of Fractions is 3/46314120.Finally, GCF of Fractions for 30/680, 75/622, 216/219 is 3/46314120.