GCF of 1705/416, 6578/6946
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1705/416, 6578/6946 i.e 11/1444768 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1705/416, 6578/6946.
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 1705/416,6578/6946?
Given fractions are 1705/416,6578/6946
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 1705/416,6578/6946, numerators are 1705,6578
Denominators are 416,6946
The GCF of 1705,6578 is 11 .
LCM of 416,6946 is 1444768.
The greatest common factor of 1705/416,6578/6946 = [GCF of 1705,6578]/[LCM of 416,6946]= 11/1444768
Therefore, the GCF of 1705/416,6578/6946 is 11/1444768.
To find the highest common factor of 1705,6578, we have to find the factors of both numbers and list the highest common factor.
The factors of 1705 are 1, 5, 11, 31, 55, 155, 341, 1705
The factors of 6578 are 1, 2, 11, 13, 22, 23, 26, 46, 143, 253, 286, 299, 506, 598, 3289, 6578
The HCF of 1705,6578 is 11.
Lets's calculate GCF of 1705,6578
| 11 | 1705, 6578 |
| 155, 598 |
∴ So the GCF of the given numbers is 11 = 11
Greatest Common Factor of 1705,6578 By Matching Biggest Common Factor Method
Now, list down the factors of 1705
:1,5,11,31,55,155,341,1705
Now, list down the factors of 6578
:1,2,11,13,22,23,26,46,143,253,286,299,506,598,3289,6578
Greatest Common Factor
We found the factors 1705,6578 . The biggest common factor number is the GCF number.
So the greatest common factor 1705,6578 is 11.
Lets's calculate LCM of 416,6946
| 2 | 416, 6946 |
| 208, 3473 |
∴ So the LCM of the given numbers is 2 x 208 x 3473 = 1444768
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 11/1444768
Therefore, the GCF of Fractions 1705/416,6578/6946 is 11/1444768
Least Common Multiple of 416,6946 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 416,6946 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(416,6946) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(416,6946) x common factors =2 x 1 = 2
LCM(416,6946) = ( 416 × 6946 ) / 2
LCM(416,6946) = 2889536 / 2
LCM(416,6946) = 1444768
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FAQs on GCF of Fractions of 1705/416, 6578/6946
1. What is the HCF of 1705,6578?
The HCF of 1705,6578 is 11
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 1705/416, 6578/6946?
Answer: GCF of Numerators as per given numbers 1705/416, 6578/6946 is
GCF of Numerators i.e. for 1705,6578 is 11
LCM of denominators i.e. for 416,6946 is 1444768.
Thus, GCF of Fractions is 11/1444768.Finally, GCF of Fractions for 1705/416, 6578/6946 is 11/1444768.