GCF of 812/748, 9205/617
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 812/748, 9205/617 i.e 7/461516 easily. The following is the detailed procedure to determine the greatest common factor of fractions 812/748, 9205/617.
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 812/748,9205/617?
Given fractions are 812/748,9205/617
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 812/748,9205/617, numerators are 812,9205
Denominators are 748,617
The GCF of 812,9205 is 7 .
LCM of 748,617 is 461516.
The greatest common factor of 812/748,9205/617 = [GCF of 812,9205]/[LCM of 748,617]= 7/461516
Therefore, the GCF of 812/748,9205/617 is 7/461516.
To find the highest common factor of 812,9205, we have to find the factors of both numbers and list the highest common factor.
The factors of 812 are 1, 2, 4, 7, 14, 28, 29, 58, 116, 203, 406, 812
The factors of 9205 are 1, 5, 7, 35, 263, 1315, 1841, 9205
The HCF of 812,9205 is 7.
Lets's calculate GCF of 812,9205
| 7 | 812, 9205 |
| 116, 1315 |
∴ So the GCF of the given numbers is 7 = 7
Greatest Common Factor of 812,9205 By Matching Biggest Common Factor Method
Now, list down the factors of 812
:1,2,4,7,14,28,29,58,116,203,406,812
Now, list down the factors of 9205
:1,5,7,35,263,1315,1841,9205
Greatest Common Factor
We found the factors 812,9205 . The biggest common factor number is the GCF number.
So the greatest common factor 812,9205 is 7.
Lets's calculate LCM of 748,617
Given numbers has no common factors except 1. So, there LCM is their product i.e 461516
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 7/461516
Therefore, the GCF of Fractions 812/748,9205/617 is 7/461516
Least Common Multiple of 748,617 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 748,617 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(748,617) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(748,617) x common factors =1 x 1 = 1
LCM(748,617) = ( 748 × 617 ) / 1
LCM(748,617) = 461516 / 1
LCM(748,617) = 461516
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FAQs on GCF of Fractions of 812/748, 9205/617
1. What is the HCF of 812,9205?
The HCF of 812,9205 is 7
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 812/748, 9205/617?
Answer: GCF of Numerators as per given numbers 812/748, 9205/617 is
GCF of Numerators i.e. for 812,9205 is 7
LCM of denominators i.e. for 748,617 is 461516.
Thus, GCF of Fractions is 7/461516.Finally, GCF of Fractions for 812/748, 9205/617 is 7/461516.