GCF of 71/64, 120/60, 219/473
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 71/64, 120/60, 219/473 i.e 1/454080 easily. The following is the detailed procedure to determine the greatest common factor of fractions 71/64, 120/60, 219/473.
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 71/64,120/60,219/473?
Given fractions are 71/64,120/60,219/473
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 71/64,120/60,219/473, numerators are 71,120,219
Denominators are 64,60,473
The GCF of 71,120,219 is 1 .
LCM of 64,60,473 is 454080.
The greatest common factor of 71/64,120/60,219/473 = [GCF of 71,120,219]/[LCM of 64,60,473]= 1/454080
Therefore, the GCF of 71/64,120/60,219/473 is 1/454080.
To find the highest common factor of 71,120,219, we have to find the factors of both numbers and list the highest common factor.
The factors of 71 are 1, 71
The factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
The factors of 219 are 1, 3, 73, 219
The HCF of 71,120,219 is 1.
Lets's calculate GCF of 71,120,219
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 71,120,219 By Matching Biggest Common Factor Method
Now, list down the factors of 71
:1,71
Now, list down the factors of 120
:1,2,3,4,5,6,8,10,12,15,20,24,30,40,60,120
Now, list down the factors of 219
:1,3,73,219
Greatest Common Factor
We found the factors 71,120,219 . The biggest common factor number is the GCF number.
So the greatest common factor 71,120,219 is 1.
Lets's calculate LCM of 64,60,473
| 2 | 64, 60, 473 |
| 2 | 32, 30, 473 |
| 16, 15, 473 |
∴ So the LCM of the given numbers is 2 x 2 x 16 x 15 x 473 = 454080
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/454080
Therefore, the GCF of Fractions 71/64,120/60,219/473 is 1/454080
Least Common Multiple of 64,60,473 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 64,60,473 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(64,60,473) = 1
common factors(in case of two or more numbers have common factors) = 4
GCF(64,60,473) x common factors =1 x 4 = 4
LCM(64,60,473) = ( 64 × 60 × 473 ) / 4
LCM(64,60,473) = 1816320 / 4
LCM(64,60,473) = 454080
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FAQs on GCF of Fractions of 71/64, 120/60, 219/473
1. What is the HCF of 71,120,219?
The HCF of 71,120,219 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 71/64, 120/60, 219/473?
Answer: GCF of Numerators as per given numbers 71/64, 120/60, 219/473 is
GCF of Numerators i.e. for 71,120,219 is 1
LCM of denominators i.e. for 64,60,473 is 454080.
Thus, GCF of Fractions is 1/454080.Finally, GCF of Fractions for 71/64, 120/60, 219/473 is 1/454080.