GCF of 678/78, 660/182
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 678/78, 660/182 i.e 6/546 easily. The following is the detailed procedure to determine the greatest common factor of fractions 678/78, 660/182.
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 678/78,660/182?
Given fractions are 678/78,660/182
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 678/78,660/182, numerators are 678,660
Denominators are 78,182
The GCF of 678,660 is 6 .
LCM of 78,182 is 546.
The greatest common factor of 678/78,660/182 = [GCF of 678,660]/[LCM of 78,182]= 6/546
Therefore, the GCF of 678/78,660/182 is 6/546.
To find the highest common factor of 678,660, we have to find the factors of both numbers and list the highest common factor.
The factors of 678 are 1, 2, 3, 6, 113, 226, 339, 678
The factors of 660 are 1, 2, 3, 4, 5, 6, 10, 11, 12, 15, 20, 22, 30, 33, 44, 55, 60, 66, 110, 132, 165, 220, 330, 660
The HCF of 678,660 is 6.
Lets's calculate GCF of 678,660
| 2 | 678, 660 |
| 3 | 339, 330 |
| 113, 110 |
∴ So the GCF of the given numbers is 2 x 3 = 6
Greatest Common Factor of 678,660 By Matching Biggest Common Factor Method
Now, list down the factors of 678
:1,2,3,6,113,226,339,678
Now, list down the factors of 660
:1,2,3,4,5,6,10,11,12,15,20,22,30,33,44,55,60,66,110,132,165,220,330,660
Greatest Common Factor
We found the factors 678,660 . The biggest common factor number is the GCF number.
So the greatest common factor 678,660 is 6.
Lets's calculate LCM of 78,182
| 2 | 78, 182 |
| 13 | 39, 91 |
| 3, 7 |
∴ So the LCM of the given numbers is 2 x 13 x 3 x 7 = 546
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/546
Therefore, the GCF of Fractions 678/78,660/182 is 6/546
Least Common Multiple of 78,182 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 78,182 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(78,182) = 26
common factors(in case of two or more numbers have common factors) = 1
GCF(78,182) x common factors =26 x 1 = 26
LCM(78,182) = ( 78 × 182 ) / 26
LCM(78,182) = 14196 / 26
LCM(78,182) = 546
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FAQs on GCF of Fractions of 678/78, 660/182
1. What is the HCF of 678,660?
The HCF of 678,660 is 6
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 678/78, 660/182?
Answer: GCF of Numerators as per given numbers 678/78, 660/182 is
GCF of Numerators i.e. for 678,660 is 6
LCM of denominators i.e. for 78,182 is 546.
Thus, GCF of Fractions is 6/546.Finally, GCF of Fractions for 678/78, 660/182 is 6/546.