GCF of 687/218, 249/196
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 687/218, 249/196 i.e 3/21364 easily. The following is the detailed procedure to determine the greatest common factor of fractions 687/218, 249/196.
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 687/218,249/196?
Given fractions are 687/218,249/196
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 687/218,249/196, numerators are 687,249
Denominators are 218,196
The GCF of 687,249 is 3 .
LCM of 218,196 is 21364.
The greatest common factor of 687/218,249/196 = [GCF of 687,249]/[LCM of 218,196]= 3/21364
Therefore, the GCF of 687/218,249/196 is 3/21364.
To find the highest common factor of 687,249, we have to find the factors of both numbers and list the highest common factor.
The factors of 687 are 1, 3, 229, 687
The factors of 249 are 1, 3, 83, 249
The HCF of 687,249 is 3.
Lets's calculate GCF of 687,249
| 3 | 687, 249 |
| 229, 83 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 687,249 By Matching Biggest Common Factor Method
Now, list down the factors of 687
:1,3,229,687
Now, list down the factors of 249
:1,3,83,249
Greatest Common Factor
We found the factors 687,249 . The biggest common factor number is the GCF number.
So the greatest common factor 687,249 is 3.
Lets's calculate LCM of 218,196
| 2 | 218, 196 |
| 109, 98 |
∴ So the LCM of the given numbers is 2 x 109 x 98 = 21364
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/21364
Therefore, the GCF of Fractions 687/218,249/196 is 3/21364
Least Common Multiple of 218,196 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 218,196 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(218,196) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(218,196) x common factors =2 x 1 = 2
LCM(218,196) = ( 218 × 196 ) / 2
LCM(218,196) = 42728 / 2
LCM(218,196) = 21364
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FAQs on GCF of Fractions of 687/218, 249/196
1. What is the HCF of 687,249?
The HCF of 687,249 is 3
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 687/218, 249/196?
Answer: GCF of Numerators as per given numbers 687/218, 249/196 is
GCF of Numerators i.e. for 687,249 is 3
LCM of denominators i.e. for 218,196 is 21364.
Thus, GCF of Fractions is 3/21364.Finally, GCF of Fractions for 687/218, 249/196 is 3/21364.