Use our free GCF of Fractions Calculator tool to compute the GCF of 861/525, 756/465 i.e 21/16275 easily. The following is the detailed procedure to determine the greatest common factor of fractions 861/525, 756/465.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 861/525,756/465
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 861/525,756/465, numerators are 861,756
Denominators are 525,465
The GCF of 861,756 is 21 .
LCM of 525,465 is 16275.
The greatest common factor of 861/525,756/465 = [GCF of 861,756]/[LCM of 525,465]= 21/16275
Therefore, the GCF of 861/525,756/465 is 21/16275.
To find the highest common factor of 861,756, we have to find the factors of both numbers and list the highest common factor.
The factors of 861 are 1, 3, 7, 21, 41, 123, 287, 861
The factors of 756 are 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 27, 28, 36, 42, 54, 63, 84, 108, 126, 189, 252, 378, 756
The HCF of 861,756 is 21.
Lets's calculate GCF of 861,756
3 | 861, 756 |
7 | 287, 252 |
41, 36 |
∴ So the GCF of the given numbers is 3 x 7 = 21
Now, list down the factors of 861
:1,3,7,21,41,123,287,861
Now, list down the factors of 756
:1,2,3,4,6,7,9,12,14,18,21,27,28,36,42,54,63,84,108,126,189,252,378,756
Greatest Common Factor
We found the factors 861,756 . The biggest common factor number is the GCF number.
So the greatest common factor 861,756 is 21.
Lets's calculate LCM of 525,465
3 | 525, 465 |
5 | 175, 155 |
35, 31 |
∴ So the LCM of the given numbers is 3 x 5 x 35 x 31 = 16275
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 21/16275
Therefore, the GCF of Fractions 861/525,756/465 is 21/16275
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 525,465 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(525,465) = 15
common factors(in case of two or more numbers have common factors) = 1
GCF(525,465) x common factors =15 x 1 = 15
LCM(525,465) = ( 525 × 465 ) / 15
LCM(525,465) = 244125 / 15
LCM(525,465) = 16275
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 861,756?
The HCF of 861,756 is 21
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 861/525, 756/465?
Answer: GCF of Numerators as per given numbers 861/525, 756/465 is
GCF of Numerators i.e. for 861,756 is 21
LCM of denominators i.e. for 525,465 is 16275.
Thus, GCF of Fractions is 21/16275.Finally, GCF of Fractions for 861/525, 756/465 is 21/16275.