GCF of 678/76, 898/1728
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 678/76, 898/1728 i.e 2/32832 easily. The following is the detailed procedure to determine the greatest common factor of fractions 678/76, 898/1728.
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 678/76,898/1728?
Given fractions are 678/76,898/1728
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 678/76,898/1728, numerators are 678,898
Denominators are 76,1728
The GCF of 678,898 is 2 .
LCM of 76,1728 is 32832.
The greatest common factor of 678/76,898/1728 = [GCF of 678,898]/[LCM of 76,1728]= 2/32832
Therefore, the GCF of 678/76,898/1728 is 2/32832.
To find the highest common factor of 678,898, 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 898 are 1, 2, 449, 898
The HCF of 678,898 is 2.
Lets's calculate GCF of 678,898
| 2 | 678, 898 |
| 339, 449 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 678,898 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 898
:1,2,449,898
Greatest Common Factor
We found the factors 678,898 . The biggest common factor number is the GCF number.
So the greatest common factor 678,898 is 2.
Lets's calculate LCM of 76,1728
| 2 | 76, 1728 |
| 2 | 38, 864 |
| 19, 432 |
∴ So the LCM of the given numbers is 2 x 2 x 19 x 432 = 32832
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/32832
Therefore, the GCF of Fractions 678/76,898/1728 is 2/32832
Least Common Multiple of 76,1728 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 76,1728 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(76,1728) = 4
common factors(in case of two or more numbers have common factors) = 1
GCF(76,1728) x common factors =4 x 1 = 4
LCM(76,1728) = ( 76 × 1728 ) / 4
LCM(76,1728) = 131328 / 4
LCM(76,1728) = 32832
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FAQs on GCF of Fractions of 678/76, 898/1728
1. What is the HCF of 678,898?
The HCF of 678,898 is 2
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 678/76, 898/1728?
Answer: GCF of Numerators as per given numbers 678/76, 898/1728 is
GCF of Numerators i.e. for 678,898 is 2
LCM of denominators i.e. for 76,1728 is 32832.
Thus, GCF of Fractions is 2/32832.Finally, GCF of Fractions for 678/76, 898/1728 is 2/32832.