Use our free GCF of Fractions Calculator tool to compute the GCF of 442/610, 972/682 i.e 2/208010 easily. The following is the detailed procedure to determine the greatest common factor of fractions 442/610, 972/682.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 442/610,972/682
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 442/610,972/682, numerators are 442,972
Denominators are 610,682
The GCF of 442,972 is 2 .
LCM of 610,682 is 208010.
The greatest common factor of 442/610,972/682 = [GCF of 442,972]/[LCM of 610,682]= 2/208010
Therefore, the GCF of 442/610,972/682 is 2/208010.
To find the highest common factor of 442,972, we have to find the factors of both numbers and list the highest common factor.
The factors of 442 are 1, 2, 13, 17, 26, 34, 221, 442
The factors of 972 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 243, 324, 486, 972
The HCF of 442,972 is 2.
Lets's calculate GCF of 442,972
2 | 442, 972 |
221, 486 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 442
:1,2,13,17,26,34,221,442
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
Greatest Common Factor
We found the factors 442,972 . The biggest common factor number is the GCF number.
So the greatest common factor 442,972 is 2.
Lets's calculate LCM of 610,682
2 | 610, 682 |
305, 341 |
∴ So the LCM of the given numbers is 2 x 305 x 341 = 208010
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/208010
Therefore, the GCF of Fractions 442/610,972/682 is 2/208010
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 610,682 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(610,682) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(610,682) x common factors =2 x 1 = 2
LCM(610,682) = ( 610 × 682 ) / 2
LCM(610,682) = 416020 / 2
LCM(610,682) = 208010
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 442,972?
The HCF of 442,972 is 2
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 442/610, 972/682?
Answer: GCF of Numerators as per given numbers 442/610, 972/682 is
GCF of Numerators i.e. for 442,972 is 2
LCM of denominators i.e. for 610,682 is 208010.
Thus, GCF of Fractions is 2/208010.Finally, GCF of Fractions for 442/610, 972/682 is 2/208010.