GCF of 392/78, 776/419
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 392/78, 776/419 i.e 8/32682 easily. The following is the detailed procedure to determine the greatest common factor of fractions 392/78, 776/419.
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 392/78,776/419?
Given fractions are 392/78,776/419
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 392/78,776/419, numerators are 392,776
Denominators are 78,419
The GCF of 392,776 is 8 .
LCM of 78,419 is 32682.
The greatest common factor of 392/78,776/419 = [GCF of 392,776]/[LCM of 78,419]= 8/32682
Therefore, the GCF of 392/78,776/419 is 8/32682.
To find the highest common factor of 392,776, we have to find the factors of both numbers and list the highest common factor.
The factors of 392 are 1, 2, 4, 7, 8, 14, 28, 49, 56, 98, 196, 392
The factors of 776 are 1, 2, 4, 8, 97, 194, 388, 776
The HCF of 392,776 is 8.
Lets's calculate GCF of 392,776
| 2 | 392, 776 |
| 2 | 196, 388 |
| 2 | 98, 194 |
| 49, 97 |
∴ So the GCF of the given numbers is 2 x 2 x 2 = 8
Greatest Common Factor of 392,776 By Matching Biggest Common Factor Method
Now, list down the factors of 392
:1,2,4,7,8,14,28,49,56,98,196,392
Now, list down the factors of 776
:1,2,4,8,97,194,388,776
Greatest Common Factor
We found the factors 392,776 . The biggest common factor number is the GCF number.
So the greatest common factor 392,776 is 8.
Lets's calculate LCM of 78,419
Given numbers has no common factors except 1. So, there LCM is their product i.e 32682
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 8/32682
Therefore, the GCF of Fractions 392/78,776/419 is 8/32682
Least Common Multiple of 78,419 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 78,419 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(78,419) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(78,419) x common factors =1 x 1 = 1
LCM(78,419) = ( 78 × 419 ) / 1
LCM(78,419) = 32682 / 1
LCM(78,419) = 32682
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 392/78, 776/419
1. What is the HCF of 392,776?
The HCF of 392,776 is 8
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 392/78, 776/419?
Answer: GCF of Numerators as per given numbers 392/78, 776/419 is
GCF of Numerators i.e. for 392,776 is 8
LCM of denominators i.e. for 78,419 is 32682.
Thus, GCF of Fractions is 8/32682.Finally, GCF of Fractions for 392/78, 776/419 is 8/32682.