GCF of 6767/564, 3978/171
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 6767/564, 3978/171 i.e 1/32148 easily. The following is the detailed procedure to determine the greatest common factor of fractions 6767/564, 3978/171.
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 6767/564,3978/171?
Given fractions are 6767/564,3978/171
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 6767/564,3978/171, numerators are 6767,3978
Denominators are 564,171
The GCF of 6767,3978 is 1 .
LCM of 564,171 is 32148.
The greatest common factor of 6767/564,3978/171 = [GCF of 6767,3978]/[LCM of 564,171]= 1/32148
Therefore, the GCF of 6767/564,3978/171 is 1/32148.
To find the highest common factor of 6767,3978, we have to find the factors of both numbers and list the highest common factor.
The factors of 6767 are 1, 67, 101, 6767
The factors of 3978 are 1, 2, 3, 6, 9, 13, 17, 18, 26, 34, 39, 51, 78, 102, 117, 153, 221, 234, 306, 442, 663, 1326, 1989, 3978
The HCF of 6767,3978 is 1.
Lets's calculate GCF of 6767,3978
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 6767,3978 By Matching Biggest Common Factor Method
Now, list down the factors of 6767
:1,67,101,6767
Now, list down the factors of 3978
:1,2,3,6,9,13,17,18,26,34,39,51,78,102,117,153,221,234,306,442,663,1326,1989,3978
Greatest Common Factor
We found the factors 6767,3978 . The biggest common factor number is the GCF number.
So the greatest common factor 6767,3978 is 1.
Lets's calculate LCM of 564,171
| 3 | 564, 171 |
| 188, 57 |
∴ So the LCM of the given numbers is 3 x 188 x 57 = 32148
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/32148
Therefore, the GCF of Fractions 6767/564,3978/171 is 1/32148
Least Common Multiple of 564,171 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 564,171 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(564,171) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(564,171) x common factors =3 x 1 = 3
LCM(564,171) = ( 564 × 171 ) / 3
LCM(564,171) = 96444 / 3
LCM(564,171) = 32148
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FAQs on GCF of Fractions of 6767/564, 3978/171
1. What is the HCF of 6767,3978?
The HCF of 6767,3978 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 6767/564, 3978/171?
Answer: GCF of Numerators as per given numbers 6767/564, 3978/171 is
GCF of Numerators i.e. for 6767,3978 is 1
LCM of denominators i.e. for 564,171 is 32148.
Thus, GCF of Fractions is 1/32148.Finally, GCF of Fractions for 6767/564, 3978/171 is 1/32148.