Use our free GCF of Fractions Calculator tool to compute the GCF of 972/269, 429/686 i.e 3/184534 easily. The following is the detailed procedure to determine the greatest common factor of fractions 972/269, 429/686.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 972/269,429/686
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 972/269,429/686, numerators are 972,429
Denominators are 269,686
The GCF of 972,429 is 3 .
LCM of 269,686 is 184534.
The greatest common factor of 972/269,429/686 = [GCF of 972,429]/[LCM of 269,686]= 3/184534
Therefore, the GCF of 972/269,429/686 is 3/184534.
To find the highest common factor of 972,429, we have to find the factors of both numbers and list the highest common factor.
The factors of 972 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 243, 324, 486, 972
The factors of 429 are 1, 3, 11, 13, 33, 39, 143, 429
The HCF of 972,429 is 3.
Lets's calculate GCF of 972,429
3 | 972, 429 |
324, 143 |
∴ So the GCF of the given numbers is 3 = 3
Now, list down the factors of 972
:1,2,3,4,6,9,12,18,27,36,54,81,108,162,243,324,486,972
Now, list down the factors of 429
:1,3,11,13,33,39,143,429
Greatest Common Factor
We found the factors 972,429 . The biggest common factor number is the GCF number.
So the greatest common factor 972,429 is 3.
Lets's calculate LCM of 269,686
Given numbers has no common factors except 1. So, there LCM is their product i.e 184534
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/184534
Therefore, the GCF of Fractions 972/269,429/686 is 3/184534
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 269,686 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(269,686) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(269,686) x common factors =1 x 1 = 1
LCM(269,686) = ( 269 × 686 ) / 1
LCM(269,686) = 184534 / 1
LCM(269,686) = 184534
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 972,429?
The HCF of 972,429 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 972/269, 429/686?
Answer: GCF of Numerators as per given numbers 972/269, 429/686 is
GCF of Numerators i.e. for 972,429 is 3
LCM of denominators i.e. for 269,686 is 184534.
Thus, GCF of Fractions is 3/184534.Finally, GCF of Fractions for 972/269, 429/686 is 3/184534.