GCF of 9717/972, 6078/6176
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 9717/972, 6078/6176 i.e 3/1500768 easily. The following is the detailed procedure to determine the greatest common factor of fractions 9717/972, 6078/6176.
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 9717/972,6078/6176?
Given fractions are 9717/972,6078/6176
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 9717/972,6078/6176, numerators are 9717,6078
Denominators are 972,6176
The GCF of 9717,6078 is 3 .
LCM of 972,6176 is 1500768.
The greatest common factor of 9717/972,6078/6176 = [GCF of 9717,6078]/[LCM of 972,6176]= 3/1500768
Therefore, the GCF of 9717/972,6078/6176 is 3/1500768.
To find the highest common factor of 9717,6078, we have to find the factors of both numbers and list the highest common factor.
The factors of 9717 are 1, 3, 41, 79, 123, 237, 3239, 9717
The factors of 6078 are 1, 2, 3, 6, 1013, 2026, 3039, 6078
The HCF of 9717,6078 is 3.
Lets's calculate GCF of 9717,6078
| 3 | 9717, 6078 |
| 3239, 2026 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 9717,6078 By Matching Biggest Common Factor Method
Now, list down the factors of 9717
:1,3,41,79,123,237,3239,9717
Now, list down the factors of 6078
:1,2,3,6,1013,2026,3039,6078
Greatest Common Factor
We found the factors 9717,6078 . The biggest common factor number is the GCF number.
So the greatest common factor 9717,6078 is 3.
Lets's calculate LCM of 972,6176
| 2 | 972, 6176 |
| 2 | 486, 3088 |
| 243, 1544 |
∴ So the LCM of the given numbers is 2 x 2 x 243 x 1544 = 1500768
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/1500768
Therefore, the GCF of Fractions 9717/972,6078/6176 is 3/1500768
Least Common Multiple of 972,6176 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 972,6176 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(972,6176) = 4
common factors(in case of two or more numbers have common factors) = 1
GCF(972,6176) x common factors =4 x 1 = 4
LCM(972,6176) = ( 972 × 6176 ) / 4
LCM(972,6176) = 6003072 / 4
LCM(972,6176) = 1500768
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FAQs on GCF of Fractions of 9717/972, 6078/6176
1. What is the HCF of 9717,6078?
The HCF of 9717,6078 is 3
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 9717/972, 6078/6176?
Answer: GCF of Numerators as per given numbers 9717/972, 6078/6176 is
GCF of Numerators i.e. for 9717,6078 is 3
LCM of denominators i.e. for 972,6176 is 1500768.
Thus, GCF of Fractions is 3/1500768.Finally, GCF of Fractions for 9717/972, 6078/6176 is 3/1500768.