GCF of 814/74, 783/972
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 814/74, 783/972 i.e 1/35964 easily. The following is the detailed procedure to determine the greatest common factor of fractions 814/74, 783/972.
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 814/74,783/972?
Given fractions are 814/74,783/972
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 814/74,783/972, numerators are 814,783
Denominators are 74,972
The GCF of 814,783 is 1 .
LCM of 74,972 is 35964.
The greatest common factor of 814/74,783/972 = [GCF of 814,783]/[LCM of 74,972]= 1/35964
Therefore, the GCF of 814/74,783/972 is 1/35964.
To find the highest common factor of 814,783, we have to find the factors of both numbers and list the highest common factor.
The factors of 814 are 1, 2, 11, 22, 37, 74, 407, 814
The factors of 783 are 1, 3, 9, 27, 29, 87, 261, 783
The HCF of 814,783 is 1.
Lets's calculate GCF of 814,783
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 814,783 By Matching Biggest Common Factor Method
Now, list down the factors of 814
:1,2,11,22,37,74,407,814
Now, list down the factors of 783
:1,3,9,27,29,87,261,783
Greatest Common Factor
We found the factors 814,783 . The biggest common factor number is the GCF number.
So the greatest common factor 814,783 is 1.
Lets's calculate LCM of 74,972
| 2 | 74, 972 |
| 37, 486 |
∴ So the LCM of the given numbers is 2 x 37 x 486 = 35964
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/35964
Therefore, the GCF of Fractions 814/74,783/972 is 1/35964
Least Common Multiple of 74,972 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 74,972 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(74,972) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(74,972) x common factors =2 x 1 = 2
LCM(74,972) = ( 74 × 972 ) / 2
LCM(74,972) = 71928 / 2
LCM(74,972) = 35964
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 814/74, 783/972
1. What is the HCF of 814,783?
The HCF of 814,783 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 814/74, 783/972?
Answer: GCF of Numerators as per given numbers 814/74, 783/972 is
GCF of Numerators i.e. for 814,783 is 1
LCM of denominators i.e. for 74,972 is 35964.
Thus, GCF of Fractions is 1/35964.Finally, GCF of Fractions for 814/74, 783/972 is 1/35964.