GCF of 286/343, 7172/175
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 286/343, 7172/175 i.e 22/8575 easily. The following is the detailed procedure to determine the greatest common factor of fractions 286/343, 7172/175.
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 286/343,7172/175?
Given fractions are 286/343,7172/175
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 286/343,7172/175, numerators are 286,7172
Denominators are 343,175
The GCF of 286,7172 is 22 .
LCM of 343,175 is 8575.
The greatest common factor of 286/343,7172/175 = [GCF of 286,7172]/[LCM of 343,175]= 22/8575
Therefore, the GCF of 286/343,7172/175 is 22/8575.
To find the highest common factor of 286,7172, we have to find the factors of both numbers and list the highest common factor.
The factors of 286 are 1, 2, 11, 13, 22, 26, 143, 286
The factors of 7172 are 1, 2, 4, 11, 22, 44, 163, 326, 652, 1793, 3586, 7172
The HCF of 286,7172 is 22.
Lets's calculate GCF of 286,7172
| 2 | 286, 7172 |
| 11 | 143, 3586 |
| 13, 326 |
∴ So the GCF of the given numbers is 2 x 11 = 22
Greatest Common Factor of 286,7172 By Matching Biggest Common Factor Method
Now, list down the factors of 286
:1,2,11,13,22,26,143,286
Now, list down the factors of 7172
:1,2,4,11,22,44,163,326,652,1793,3586,7172
Greatest Common Factor
We found the factors 286,7172 . The biggest common factor number is the GCF number.
So the greatest common factor 286,7172 is 22.
Lets's calculate LCM of 343,175
| 7 | 343, 175 |
| 49, 25 |
∴ So the LCM of the given numbers is 7 x 49 x 25 = 8575
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 22/8575
Therefore, the GCF of Fractions 286/343,7172/175 is 22/8575
Least Common Multiple of 343,175 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 343,175 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(343,175) = 7
common factors(in case of two or more numbers have common factors) = 1
GCF(343,175) x common factors =7 x 1 = 7
LCM(343,175) = ( 343 × 175 ) / 7
LCM(343,175) = 60025 / 7
LCM(343,175) = 8575
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FAQs on GCF of Fractions of 286/343, 7172/175
1. What is the HCF of 286,7172?
The HCF of 286,7172 is 22
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 286/343, 7172/175?
Answer: GCF of Numerators as per given numbers 286/343, 7172/175 is
GCF of Numerators i.e. for 286,7172 is 22
LCM of denominators i.e. for 343,175 is 8575.
Thus, GCF of Fractions is 22/8575.Finally, GCF of Fractions for 286/343, 7172/175 is 22/8575.