GCF of 1469/629, 3978/728
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1469/629, 3978/728 i.e 13/457912 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1469/629, 3978/728.
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 1469/629,3978/728?
Given fractions are 1469/629,3978/728
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 1469/629,3978/728, numerators are 1469,3978
Denominators are 629,728
The GCF of 1469,3978 is 13 .
LCM of 629,728 is 457912.
The greatest common factor of 1469/629,3978/728 = [GCF of 1469,3978]/[LCM of 629,728]= 13/457912
Therefore, the GCF of 1469/629,3978/728 is 13/457912.
To find the highest common factor of 1469,3978, we have to find the factors of both numbers and list the highest common factor.
The factors of 1469 are 1, 13, 113, 1469
The factors of 3978 are 1, 2, 3, 6, 9, 13, 17, 18, 26, 34, 39, 51, 78, 102, 117, 153, 221, 234, 306, 442, 663, 1326, 1989, 3978
The HCF of 1469,3978 is 13.
Lets's calculate GCF of 1469,3978
| 13 | 1469, 3978 |
| 113, 306 |
∴ So the GCF of the given numbers is 13 = 13
Greatest Common Factor of 1469,3978 By Matching Biggest Common Factor Method
Now, list down the factors of 1469
:1,13,113,1469
Now, list down the factors of 3978
:1,2,3,6,9,13,17,18,26,34,39,51,78,102,117,153,221,234,306,442,663,1326,1989,3978
Greatest Common Factor
We found the factors 1469,3978 . The biggest common factor number is the GCF number.
So the greatest common factor 1469,3978 is 13.
Lets's calculate LCM of 629,728
Given numbers has no common factors except 1. So, there LCM is their product i.e 457912
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 13/457912
Therefore, the GCF of Fractions 1469/629,3978/728 is 13/457912
Least Common Multiple of 629,728 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 629,728 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(629,728) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(629,728) x common factors =1 x 1 = 1
LCM(629,728) = ( 629 × 728 ) / 1
LCM(629,728) = 457912 / 1
LCM(629,728) = 457912
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FAQs on GCF of Fractions of 1469/629, 3978/728
1. What is the HCF of 1469,3978?
The HCF of 1469,3978 is 13
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 1469/629, 3978/728?
Answer: GCF of Numerators as per given numbers 1469/629, 3978/728 is
GCF of Numerators i.e. for 1469,3978 is 13
LCM of denominators i.e. for 629,728 is 457912.
Thus, GCF of Fractions is 13/457912.Finally, GCF of Fractions for 1469/629, 3978/728 is 13/457912.