GCF of 7769/654, 8912/768
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 7769/654, 8912/768 i.e 1/83712 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7769/654, 8912/768.
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 7769/654,8912/768?
Given fractions are 7769/654,8912/768
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 7769/654,8912/768, numerators are 7769,8912
Denominators are 654,768
The GCF of 7769,8912 is 1 .
LCM of 654,768 is 83712.
The greatest common factor of 7769/654,8912/768 = [GCF of 7769,8912]/[LCM of 654,768]= 1/83712
Therefore, the GCF of 7769/654,8912/768 is 1/83712.
To find the highest common factor of 7769,8912, we have to find the factors of both numbers and list the highest common factor.
The factors of 7769 are 1, 17, 457, 7769
The factors of 8912 are 1, 2, 4, 8, 16, 557, 1114, 2228, 4456, 8912
The HCF of 7769,8912 is 1.
Lets's calculate GCF of 7769,8912
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 7769,8912 By Matching Biggest Common Factor Method
Now, list down the factors of 7769
:1,17,457,7769
Now, list down the factors of 8912
:1,2,4,8,16,557,1114,2228,4456,8912
Greatest Common Factor
We found the factors 7769,8912 . The biggest common factor number is the GCF number.
So the greatest common factor 7769,8912 is 1.
Lets's calculate LCM of 654,768
| 2 | 654, 768 |
| 3 | 327, 384 |
| 109, 128 |
∴ So the LCM of the given numbers is 2 x 3 x 109 x 128 = 83712
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/83712
Therefore, the GCF of Fractions 7769/654,8912/768 is 1/83712
Least Common Multiple of 654,768 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 654,768 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(654,768) = 6
common factors(in case of two or more numbers have common factors) = 1
GCF(654,768) x common factors =6 x 1 = 6
LCM(654,768) = ( 654 × 768 ) / 6
LCM(654,768) = 502272 / 6
LCM(654,768) = 83712
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FAQs on GCF of Fractions of 7769/654, 8912/768
1. What is the HCF of 7769,8912?
The HCF of 7769,8912 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 7769/654, 8912/768?
Answer: GCF of Numerators as per given numbers 7769/654, 8912/768 is
GCF of Numerators i.e. for 7769,8912 is 1
LCM of denominators i.e. for 654,768 is 83712.
Thus, GCF of Fractions is 1/83712.Finally, GCF of Fractions for 7769/654, 8912/768 is 1/83712.