GCF of 70/70, 644/91, 686/249
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 70/70, 644/91, 686/249 i.e 14/226590 easily. The following is the detailed procedure to determine the greatest common factor of fractions 70/70, 644/91, 686/249.
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 70/70,644/91,686/249?
Given fractions are 70/70,644/91,686/249
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 70/70,644/91,686/249, numerators are 70,644,686
Denominators are 70,91,249
The GCF of 70,644,686 is 14 .
LCM of 70,91,249 is 226590.
The greatest common factor of 70/70,644/91,686/249 = [GCF of 70,644,686]/[LCM of 70,91,249]= 14/226590
Therefore, the GCF of 70/70,644/91,686/249 is 14/226590.
To find the highest common factor of 70,644,686, we have to find the factors of both numbers and list the highest common factor.
The factors of 70 are 1, 2, 5, 7, 10, 14, 35, 70
The factors of 644 are 1, 2, 4, 7, 14, 23, 28, 46, 92, 161, 322, 644
The factors of 686 are 1, 2, 7, 14, 49, 98, 343, 686
The HCF of 70,644,686 is 14.
Lets's calculate GCF of 70,644,686
| 2 | 70, 644, 686 |
| 7 | 35, 322, 343 |
| 5, 46, 49 |
∴ So the GCF of the given numbers is 2 x 7 = 14
Greatest Common Factor of 70,644,686 By Matching Biggest Common Factor Method
Now, list down the factors of 70
:1,2,5,7,10,14,35,70
Now, list down the factors of 644
:1,2,4,7,14,23,28,46,92,161,322,644
Now, list down the factors of 686
:1,2,7,14,49,98,343,686
Greatest Common Factor
We found the factors 70,644,686 . The biggest common factor number is the GCF number.
So the greatest common factor 70,644,686 is 14.
Lets's calculate LCM of 70,91,249
| 7 | 70, 91, 249 |
| 10, 13, 249 |
∴ So the LCM of the given numbers is 7 x 10 x 13 x 249 = 226590
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 14/226590
Therefore, the GCF of Fractions 70/70,644/91,686/249 is 14/226590
Least Common Multiple of 70,91,249 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 70,91,249 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(70,91,249) = 1
common factors(in case of two or more numbers have common factors) = 7
GCF(70,91,249) x common factors =1 x 7 = 7
LCM(70,91,249) = ( 70 × 91 × 249 ) / 7
LCM(70,91,249) = 1586130 / 7
LCM(70,91,249) = 226590
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FAQs on GCF of Fractions of 70/70, 644/91, 686/249
1. What is the HCF of 70,644,686?
The HCF of 70,644,686 is 14
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 70/70, 644/91, 686/249?
Answer: GCF of Numerators as per given numbers 70/70, 644/91, 686/249 is
GCF of Numerators i.e. for 70,644,686 is 14
LCM of denominators i.e. for 70,91,249 is 226590.
Thus, GCF of Fractions is 14/226590.Finally, GCF of Fractions for 70/70, 644/91, 686/249 is 14/226590.