GCF of 967/78, 709/93, 204/82
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 967/78, 709/93, 204/82 i.e 1/99138 easily. The following is the detailed procedure to determine the greatest common factor of fractions 967/78, 709/93, 204/82.
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 967/78,709/93,204/82?
Given fractions are 967/78,709/93,204/82
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 967/78,709/93,204/82, numerators are 967,709,204
Denominators are 78,93,82
The GCF of 967,709,204 is 1 .
LCM of 78,93,82 is 99138.
The greatest common factor of 967/78,709/93,204/82 = [GCF of 967,709,204]/[LCM of 78,93,82]= 1/99138
Therefore, the GCF of 967/78,709/93,204/82 is 1/99138.
To find the highest common factor of 967,709,204, we have to find the factors of both numbers and list the highest common factor.
The factors of 967 are 1, 967
The factors of 709 are 1, 709
The factors of 204 are 1, 2, 3, 4, 6, 12, 17, 34, 51, 68, 102, 204
The HCF of 967,709,204 is 1.
Lets's calculate GCF of 967,709,204
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 967,709,204 By Matching Biggest Common Factor Method
Now, list down the factors of 967
:1,967
Now, list down the factors of 709
:1,709
Now, list down the factors of 204
:1,2,3,4,6,12,17,34,51,68,102,204
Greatest Common Factor
We found the factors 967,709,204 . The biggest common factor number is the GCF number.
So the greatest common factor 967,709,204 is 1.
Lets's calculate LCM of 78,93,82
| 2 | 78, 93, 82 |
| 3 | 39, 93, 41 |
| 13, 31, 41 |
∴ So the LCM of the given numbers is 2 x 3 x 13 x 31 x 41 = 99138
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/99138
Therefore, the GCF of Fractions 967/78,709/93,204/82 is 1/99138
Least Common Multiple of 78,93,82 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 78,93,82 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(78,93,82) = 1
common factors(in case of two or more numbers have common factors) = 6
GCF(78,93,82) x common factors =1 x 6 = 6
LCM(78,93,82) = ( 78 × 93 × 82 ) / 6
LCM(78,93,82) = 594828 / 6
LCM(78,93,82) = 99138
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FAQs on GCF of Fractions of 967/78, 709/93, 204/82
1. What is the HCF of 967,709,204?
The HCF of 967,709,204 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 967/78, 709/93, 204/82?
Answer: GCF of Numerators as per given numbers 967/78, 709/93, 204/82 is
GCF of Numerators i.e. for 967,709,204 is 1
LCM of denominators i.e. for 78,93,82 is 99138.
Thus, GCF of Fractions is 1/99138.Finally, GCF of Fractions for 967/78, 709/93, 204/82 is 1/99138.