GCF of 1566/819, 1296/706
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1566/819, 1296/706 i.e 54/578214 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1566/819, 1296/706.
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 1566/819,1296/706?
Given fractions are 1566/819,1296/706
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 1566/819,1296/706, numerators are 1566,1296
Denominators are 819,706
The GCF of 1566,1296 is 54 .
LCM of 819,706 is 578214.
The greatest common factor of 1566/819,1296/706 = [GCF of 1566,1296]/[LCM of 819,706]= 54/578214
Therefore, the GCF of 1566/819,1296/706 is 54/578214.
To find the highest common factor of 1566,1296, we have to find the factors of both numbers and list the highest common factor.
The factors of 1566 are 1, 2, 3, 6, 9, 18, 27, 29, 54, 58, 87, 174, 261, 522, 783, 1566
The factors of 1296 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 36, 48, 54, 72, 81, 108, 144, 162, 216, 324, 432, 648, 1296
The HCF of 1566,1296 is 54.
Lets's calculate GCF of 1566,1296
| 2 | 1566, 1296 |
| 3 | 783, 648 |
| 3 | 261, 216 |
| 3 | 87, 72 |
| 29, 24 |
∴ So the GCF of the given numbers is 2 x 3 x 3 x 3 = 54
Greatest Common Factor of 1566,1296 By Matching Biggest Common Factor Method
Now, list down the factors of 1566
:1,2,3,6,9,18,27,29,54,58,87,174,261,522,783,1566
Now, list down the factors of 1296
:1,2,3,4,6,8,9,12,16,18,24,27,36,48,54,72,81,108,144,162,216,324,432,648,1296
Greatest Common Factor
We found the factors 1566,1296 . The biggest common factor number is the GCF number.
So the greatest common factor 1566,1296 is 54.
Lets's calculate LCM of 819,706
Given numbers has no common factors except 1. So, there LCM is their product i.e 578214
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 54/578214
Therefore, the GCF of Fractions 1566/819,1296/706 is 54/578214
Least Common Multiple of 819,706 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 819,706 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(819,706) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(819,706) x common factors =1 x 1 = 1
LCM(819,706) = ( 819 × 706 ) / 1
LCM(819,706) = 578214 / 1
LCM(819,706) = 578214
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FAQs on GCF of Fractions of 1566/819, 1296/706
1. What is the HCF of 1566,1296?
The HCF of 1566,1296 is 54
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 1566/819, 1296/706?
Answer: GCF of Numerators as per given numbers 1566/819, 1296/706 is
GCF of Numerators i.e. for 1566,1296 is 54
LCM of denominators i.e. for 819,706 is 578214.
Thus, GCF of Fractions is 54/578214.Finally, GCF of Fractions for 1566/819, 1296/706 is 54/578214.