GCF of 408/346, 544/720
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 408/346, 544/720 i.e 136/124560 easily. The following is the detailed procedure to determine the greatest common factor of fractions 408/346, 544/720.
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 408/346,544/720?
Given fractions are 408/346,544/720
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 408/346,544/720, numerators are 408,544
Denominators are 346,720
The GCF of 408,544 is 136 .
LCM of 346,720 is 124560.
The greatest common factor of 408/346,544/720 = [GCF of 408,544]/[LCM of 346,720]= 136/124560
Therefore, the GCF of 408/346,544/720 is 136/124560.
To find the highest common factor of 408,544, we have to find the factors of both numbers and list the highest common factor.
The factors of 408 are 1, 2, 3, 4, 6, 8, 12, 17, 24, 34, 51, 68, 102, 136, 204, 408
The factors of 544 are 1, 2, 4, 8, 16, 17, 32, 34, 68, 136, 272, 544
The HCF of 408,544 is 136.
Lets's calculate GCF of 408,544
| 2 | 408, 544 |
| 2 | 204, 272 |
| 2 | 102, 136 |
| 17 | 51, 68 |
| 3, 4 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 17 = 136
Greatest Common Factor of 408,544 By Matching Biggest Common Factor Method
Now, list down the factors of 408
:1,2,3,4,6,8,12,17,24,34,51,68,102,136,204,408
Now, list down the factors of 544
:1,2,4,8,16,17,32,34,68,136,272,544
Greatest Common Factor
We found the factors 408,544 . The biggest common factor number is the GCF number.
So the greatest common factor 408,544 is 136.
Lets's calculate LCM of 346,720
| 2 | 346, 720 |
| 173, 360 |
∴ So the LCM of the given numbers is 2 x 173 x 360 = 124560
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 136/124560
Therefore, the GCF of Fractions 408/346,544/720 is 136/124560
Least Common Multiple of 346,720 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 346,720 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(346,720) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(346,720) x common factors =2 x 1 = 2
LCM(346,720) = ( 346 × 720 ) / 2
LCM(346,720) = 249120 / 2
LCM(346,720) = 124560
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FAQs on GCF of Fractions of 408/346, 544/720
1. What is the HCF of 408,544?
The HCF of 408,544 is 136
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 408/346, 544/720?
Answer: GCF of Numerators as per given numbers 408/346, 544/720 is
GCF of Numerators i.e. for 408,544 is 136
LCM of denominators i.e. for 346,720 is 124560.
Thus, GCF of Fractions is 136/124560.Finally, GCF of Fractions for 408/346, 544/720 is 136/124560.