GCF of 733/420, 678/321
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 733/420, 678/321 i.e 1/44940 easily. The following is the detailed procedure to determine the greatest common factor of fractions 733/420, 678/321.
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 733/420,678/321?
Given fractions are 733/420,678/321
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 733/420,678/321, numerators are 733,678
Denominators are 420,321
The GCF of 733,678 is 1 .
LCM of 420,321 is 44940.
The greatest common factor of 733/420,678/321 = [GCF of 733,678]/[LCM of 420,321]= 1/44940
Therefore, the GCF of 733/420,678/321 is 1/44940.
To find the highest common factor of 733,678, we have to find the factors of both numbers and list the highest common factor.
The factors of 733 are 1, 733
The factors of 678 are 1, 2, 3, 6, 113, 226, 339, 678
The HCF of 733,678 is 1.
Lets's calculate GCF of 733,678
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 733,678 By Matching Biggest Common Factor Method
Now, list down the factors of 733
:1,733
Now, list down the factors of 678
:1,2,3,6,113,226,339,678
Greatest Common Factor
We found the factors 733,678 . The biggest common factor number is the GCF number.
So the greatest common factor 733,678 is 1.
Lets's calculate LCM of 420,321
| 3 | 420, 321 |
| 140, 107 |
∴ So the LCM of the given numbers is 3 x 140 x 107 = 44940
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/44940
Therefore, the GCF of Fractions 733/420,678/321 is 1/44940
Least Common Multiple of 420,321 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 420,321 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(420,321) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(420,321) x common factors =3 x 1 = 3
LCM(420,321) = ( 420 × 321 ) / 3
LCM(420,321) = 134820 / 3
LCM(420,321) = 44940
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FAQs on GCF of Fractions of 733/420, 678/321
1. What is the HCF of 733,678?
The HCF of 733,678 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 733/420, 678/321?
Answer: GCF of Numerators as per given numbers 733/420, 678/321 is
GCF of Numerators i.e. for 733,678 is 1
LCM of denominators i.e. for 420,321 is 44940.
Thus, GCF of Fractions is 1/44940.Finally, GCF of Fractions for 733/420, 678/321 is 1/44940.