GCF of 72/872, 36/410, 415/461
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 72/872, 36/410, 415/461 i.e 1/82408360 easily. The following is the detailed procedure to determine the greatest common factor of fractions 72/872, 36/410, 415/461.
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 72/872,36/410,415/461?
Given fractions are 72/872,36/410,415/461
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 72/872,36/410,415/461, numerators are 72,36,415
Denominators are 872,410,461
The GCF of 72,36,415 is 1 .
LCM of 872,410,461 is 82408360.
The greatest common factor of 72/872,36/410,415/461 = [GCF of 72,36,415]/[LCM of 872,410,461]= 1/82408360
Therefore, the GCF of 72/872,36/410,415/461 is 1/82408360.
To find the highest common factor of 72,36,415, we have to find the factors of both numbers and list the highest common factor.
The factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36
The factors of 415 are 1, 5, 83, 415
The HCF of 72,36,415 is 1.
Lets's calculate GCF of 72,36,415
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 72,36,415 By Matching Biggest Common Factor Method
Now, list down the factors of 72
:1,2,3,4,6,8,9,12,18,24,36,72
Now, list down the factors of 36
:1,2,3,4,6,9,12,18,36
Now, list down the factors of 415
:1,5,83,415
Greatest Common Factor
We found the factors 72,36,415 . The biggest common factor number is the GCF number.
So the greatest common factor 72,36,415 is 1.
Lets's calculate LCM of 872,410,461
| 2 | 872, 410, 461 |
| 436, 205, 461 |
∴ So the LCM of the given numbers is 2 x 436 x 205 x 461 = 82408360
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/82408360
Therefore, the GCF of Fractions 72/872,36/410,415/461 is 1/82408360
Least Common Multiple of 872,410,461 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 872,410,461 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(872,410,461) = 1
common factors(in case of two or more numbers have common factors) = 2
GCF(872,410,461) x common factors =1 x 2 = 2
LCM(872,410,461) = ( 872 × 410 × 461 ) / 2
LCM(872,410,461) = 164816720 / 2
LCM(872,410,461) = 82408360
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FAQs on GCF of Fractions of 72/872, 36/410, 415/461
1. What is the HCF of 72,36,415?
The HCF of 72,36,415 is 1
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 72/872, 36/410, 415/461?
Answer: GCF of Numerators as per given numbers 72/872, 36/410, 415/461 is
GCF of Numerators i.e. for 72,36,415 is 1
LCM of denominators i.e. for 872,410,461 is 82408360.
Thus, GCF of Fractions is 1/82408360.Finally, GCF of Fractions for 72/872, 36/410, 415/461 is 1/82408360.