GCF of 747/458, 219/658
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 747/458, 219/658 i.e 3/150682 easily. The following is the detailed procedure to determine the greatest common factor of fractions 747/458, 219/658.
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 747/458,219/658?
Given fractions are 747/458,219/658
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 747/458,219/658, numerators are 747,219
Denominators are 458,658
The GCF of 747,219 is 3 .
LCM of 458,658 is 150682.
The greatest common factor of 747/458,219/658 = [GCF of 747,219]/[LCM of 458,658]= 3/150682
Therefore, the GCF of 747/458,219/658 is 3/150682.
To find the highest common factor of 747,219, we have to find the factors of both numbers and list the highest common factor.
The factors of 747 are 1, 3, 9, 83, 249, 747
The factors of 219 are 1, 3, 73, 219
The HCF of 747,219 is 3.
Lets's calculate GCF of 747,219
| 3 | 747, 219 |
| 249, 73 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 747,219 By Matching Biggest Common Factor Method
Now, list down the factors of 747
:1,3,9,83,249,747
Now, list down the factors of 219
:1,3,73,219
Greatest Common Factor
We found the factors 747,219 . The biggest common factor number is the GCF number.
So the greatest common factor 747,219 is 3.
Lets's calculate LCM of 458,658
| 2 | 458, 658 |
| 229, 329 |
∴ So the LCM of the given numbers is 2 x 229 x 329 = 150682
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/150682
Therefore, the GCF of Fractions 747/458,219/658 is 3/150682
Least Common Multiple of 458,658 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 458,658 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(458,658) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(458,658) x common factors =2 x 1 = 2
LCM(458,658) = ( 458 × 658 ) / 2
LCM(458,658) = 301364 / 2
LCM(458,658) = 150682
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FAQs on GCF of Fractions of 747/458, 219/658
1. What is the HCF of 747,219?
The HCF of 747,219 is 3
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 747/458, 219/658?
Answer: GCF of Numerators as per given numbers 747/458, 219/658 is
GCF of Numerators i.e. for 747,219 is 3
LCM of denominators i.e. for 458,658 is 150682.
Thus, GCF of Fractions is 3/150682.Finally, GCF of Fractions for 747/458, 219/658 is 3/150682.