GCF of 777/38, 420/595
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 777/38, 420/595 i.e 21/22610 easily. The following is the detailed procedure to determine the greatest common factor of fractions 777/38, 420/595.
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 777/38,420/595?
Given fractions are 777/38,420/595
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 777/38,420/595, numerators are 777,420
Denominators are 38,595
The GCF of 777,420 is 21 .
LCM of 38,595 is 22610.
The greatest common factor of 777/38,420/595 = [GCF of 777,420]/[LCM of 38,595]= 21/22610
Therefore, the GCF of 777/38,420/595 is 21/22610.
To find the highest common factor of 777,420, 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 420 are 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, 420
The HCF of 777,420 is 21.
Lets's calculate GCF of 777,420
| 3 | 777, 420 |
| 7 | 259, 140 |
| 37, 20 |
∴ So the GCF of the given numbers is 3 x 7 = 21
Greatest Common Factor of 777,420 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 420
:1,2,3,4,5,6,7,10,12,14,15,20,21,28,30,35,42,60,70,84,105,140,210,420
Greatest Common Factor
We found the factors 777,420 . The biggest common factor number is the GCF number.
So the greatest common factor 777,420 is 21.
Lets's calculate LCM of 38,595
Given numbers has no common factors except 1. So, there LCM is their product i.e 22610
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 21/22610
Therefore, the GCF of Fractions 777/38,420/595 is 21/22610
Least Common Multiple of 38,595 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 38,595 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(38,595) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(38,595) x common factors =1 x 1 = 1
LCM(38,595) = ( 38 × 595 ) / 1
LCM(38,595) = 22610 / 1
LCM(38,595) = 22610
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FAQs on GCF of Fractions of 777/38, 420/595
1. What is the HCF of 777,420?
The HCF of 777,420 is 21
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 777/38, 420/595?
Answer: GCF of Numerators as per given numbers 777/38, 420/595 is
GCF of Numerators i.e. for 777,420 is 21
LCM of denominators i.e. for 38,595 is 22610.
Thus, GCF of Fractions is 21/22610.Finally, GCF of Fractions for 777/38, 420/595 is 21/22610.