GCF of 777/60, 219/40, 423/16
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 777/60, 219/40, 423/16 i.e 3/240 easily. The following is the detailed procedure to determine the greatest common factor of fractions 777/60, 219/40, 423/16.
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 777/60,219/40,423/16?
Given fractions are 777/60,219/40,423/16
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 777/60,219/40,423/16, numerators are 777,219,423
Denominators are 60,40,16
The GCF of 777,219,423 is 3 .
LCM of 60,40,16 is 240.
The greatest common factor of 777/60,219/40,423/16 = [GCF of 777,219,423]/[LCM of 60,40,16]= 3/240
Therefore, the GCF of 777/60,219/40,423/16 is 3/240.
To find the highest common factor of 777,219,423, we have to find the factors of both numbers and list the highest common factor.
The factors of 777 are 1, 3, 7, 21, 37, 111, 259, 777
The factors of 219 are 1, 3, 73, 219
The factors of 423 are 1, 3, 9, 47, 141, 423
The HCF of 777,219,423 is 3.
Lets's calculate GCF of 777,219,423
| 3 | 777, 219, 423 |
| 259, 73, 141 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 777,219,423 By Matching Biggest Common Factor Method
Now, list down the factors of 777
:1,3,7,21,37,111,259,777
Now, list down the factors of 219
:1,3,73,219
Now, list down the factors of 423
:1,3,9,47,141,423
Greatest Common Factor
We found the factors 777,219,423 . The biggest common factor number is the GCF number.
So the greatest common factor 777,219,423 is 3.
Lets's calculate LCM of 60,40,16
| 2 | 60, 40, 16 |
| 2 | 30, 20, 8 |
| 2 | 15, 10, 4 |
| 5 | 15, 5, 2 |
| 3, 1, 2 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 5 x 3 x 1 x 2 = 240
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/240
Therefore, the GCF of Fractions 777/60,219/40,423/16 is 3/240
Least Common Multiple of 60,40,16 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 60,40,16 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(60,40,16) = 4
common factors(in case of two or more numbers have common factors) = 40
GCF(60,40,16) x common factors =4 x 40 = 160
LCM(60,40,16) = ( 60 × 40 × 16 ) / 160
LCM(60,40,16) = 38400 / 160
LCM(60,40,16) = 240
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FAQs on GCF of Fractions of 777/60, 219/40, 423/16
1. What is the HCF of 777,219,423?
The HCF of 777,219,423 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 777/60, 219/40, 423/16?
Answer: GCF of Numerators as per given numbers 777/60, 219/40, 423/16 is
GCF of Numerators i.e. for 777,219,423 is 3
LCM of denominators i.e. for 60,40,16 is 240.
Thus, GCF of Fractions is 3/240.Finally, GCF of Fractions for 777/60, 219/40, 423/16 is 3/240.