GCF of 766/756, 219/972
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 766/756, 219/972 i.e 1/6804 easily. The following is the detailed procedure to determine the greatest common factor of fractions 766/756, 219/972.
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 766/756,219/972?
Given fractions are 766/756,219/972
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 766/756,219/972, numerators are 766,219
Denominators are 756,972
The GCF of 766,219 is 1 .
LCM of 756,972 is 6804.
The greatest common factor of 766/756,219/972 = [GCF of 766,219]/[LCM of 756,972]= 1/6804
Therefore, the GCF of 766/756,219/972 is 1/6804.
To find the highest common factor of 766,219, we have to find the factors of both numbers and list the highest common factor.
The factors of 766 are 1, 2, 383, 766
The factors of 219 are 1, 3, 73, 219
The HCF of 766,219 is 1.
Lets's calculate GCF of 766,219
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 766,219 By Matching Biggest Common Factor Method
Now, list down the factors of 766
:1,2,383,766
Now, list down the factors of 219
:1,3,73,219
Greatest Common Factor
We found the factors 766,219 . The biggest common factor number is the GCF number.
So the greatest common factor 766,219 is 1.
Lets's calculate LCM of 756,972
| 2 | 756, 972 |
| 2 | 378, 486 |
| 3 | 189, 243 |
| 3 | 63, 81 |
| 3 | 21, 27 |
| 7, 9 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 3 x 3 x 7 x 9 = 6804
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/6804
Therefore, the GCF of Fractions 766/756,219/972 is 1/6804
Least Common Multiple of 756,972 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 756,972 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(756,972) = 108
common factors(in case of two or more numbers have common factors) = 1
GCF(756,972) x common factors =108 x 1 = 108
LCM(756,972) = ( 756 × 972 ) / 108
LCM(756,972) = 734832 / 108
LCM(756,972) = 6804
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FAQs on GCF of Fractions of 766/756, 219/972
1. What is the HCF of 766,219?
The HCF of 766,219 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 766/756, 219/972?
Answer: GCF of Numerators as per given numbers 766/756, 219/972 is
GCF of Numerators i.e. for 766,219 is 1
LCM of denominators i.e. for 756,972 is 6804.
Thus, GCF of Fractions is 1/6804.Finally, GCF of Fractions for 766/756, 219/972 is 1/6804.