GCF of 7382/714, 7814/4178
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 7382/714, 7814/4178 i.e 2/1491546 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7382/714, 7814/4178.
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 7382/714,7814/4178?
Given fractions are 7382/714,7814/4178
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 7382/714,7814/4178, numerators are 7382,7814
Denominators are 714,4178
The GCF of 7382,7814 is 2 .
LCM of 714,4178 is 1491546.
The greatest common factor of 7382/714,7814/4178 = [GCF of 7382,7814]/[LCM of 714,4178]= 2/1491546
Therefore, the GCF of 7382/714,7814/4178 is 2/1491546.
To find the highest common factor of 7382,7814, we have to find the factors of both numbers and list the highest common factor.
The factors of 7382 are 1, 2, 3691, 7382
The factors of 7814 are 1, 2, 3907, 7814
The HCF of 7382,7814 is 2.
Lets's calculate GCF of 7382,7814
| 2 | 7382, 7814 |
| 3691, 3907 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 7382,7814 By Matching Biggest Common Factor Method
Now, list down the factors of 7382
:1,2,3691,7382
Now, list down the factors of 7814
:1,2,3907,7814
Greatest Common Factor
We found the factors 7382,7814 . The biggest common factor number is the GCF number.
So the greatest common factor 7382,7814 is 2.
Lets's calculate LCM of 714,4178
| 2 | 714, 4178 |
| 357, 2089 |
∴ So the LCM of the given numbers is 2 x 357 x 2089 = 1491546
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/1491546
Therefore, the GCF of Fractions 7382/714,7814/4178 is 2/1491546
Least Common Multiple of 714,4178 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 714,4178 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(714,4178) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(714,4178) x common factors =2 x 1 = 2
LCM(714,4178) = ( 714 × 4178 ) / 2
LCM(714,4178) = 2983092 / 2
LCM(714,4178) = 1491546
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 7382/714, 7814/4178
1. What is the HCF of 7382,7814?
The HCF of 7382,7814 is 2
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 7382/714, 7814/4178?
Answer: GCF of Numerators as per given numbers 7382/714, 7814/4178 is
GCF of Numerators i.e. for 7382,7814 is 2
LCM of denominators i.e. for 714,4178 is 1491546.
Thus, GCF of Fractions is 2/1491546.Finally, GCF of Fractions for 7382/714, 7814/4178 is 2/1491546.