GCF of 1780/734, 4006/4658
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1780/734, 4006/4658 i.e 2/1709486 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1780/734, 4006/4658.
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 1780/734,4006/4658?
Given fractions are 1780/734,4006/4658
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 1780/734,4006/4658, numerators are 1780,4006
Denominators are 734,4658
The GCF of 1780,4006 is 2 .
LCM of 734,4658 is 1709486.
The greatest common factor of 1780/734,4006/4658 = [GCF of 1780,4006]/[LCM of 734,4658]= 2/1709486
Therefore, the GCF of 1780/734,4006/4658 is 2/1709486.
To find the highest common factor of 1780,4006, we have to find the factors of both numbers and list the highest common factor.
The factors of 1780 are 1, 2, 4, 5, 10, 20, 89, 178, 356, 445, 890, 1780
The factors of 4006 are 1, 2, 2003, 4006
The HCF of 1780,4006 is 2.
Lets's calculate GCF of 1780,4006
| 2 | 1780, 4006 |
| 890, 2003 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 1780,4006 By Matching Biggest Common Factor Method
Now, list down the factors of 1780
:1,2,4,5,10,20,89,178,356,445,890,1780
Now, list down the factors of 4006
:1,2,2003,4006
Greatest Common Factor
We found the factors 1780,4006 . The biggest common factor number is the GCF number.
So the greatest common factor 1780,4006 is 2.
Lets's calculate LCM of 734,4658
| 2 | 734, 4658 |
| 367, 2329 |
∴ So the LCM of the given numbers is 2 x 367 x 2329 = 1709486
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/1709486
Therefore, the GCF of Fractions 1780/734,4006/4658 is 2/1709486
Least Common Multiple of 734,4658 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 734,4658 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(734,4658) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(734,4658) x common factors =2 x 1 = 2
LCM(734,4658) = ( 734 × 4658 ) / 2
LCM(734,4658) = 3418972 / 2
LCM(734,4658) = 1709486
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FAQs on GCF of Fractions of 1780/734, 4006/4658
1. What is the HCF of 1780,4006?
The HCF of 1780,4006 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 1780/734, 4006/4658?
Answer: GCF of Numerators as per given numbers 1780/734, 4006/4658 is
GCF of Numerators i.e. for 1780,4006 is 2
LCM of denominators i.e. for 734,4658 is 1709486.
Thus, GCF of Fractions is 2/1709486.Finally, GCF of Fractions for 1780/734, 4006/4658 is 2/1709486.