Use our free GCF of Fractions Calculator tool to compute the GCF of 972/774, 639/138 i.e 9/17802 easily. The following is the detailed procedure to determine the greatest common factor of fractions 972/774, 639/138.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 972/774,639/138
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 972/774,639/138, numerators are 972,639
Denominators are 774,138
The GCF of 972,639 is 9 .
LCM of 774,138 is 17802.
The greatest common factor of 972/774,639/138 = [GCF of 972,639]/[LCM of 774,138]= 9/17802
Therefore, the GCF of 972/774,639/138 is 9/17802.
To find the highest common factor of 972,639, 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 639 are 1, 3, 9, 71, 213, 639
The HCF of 972,639 is 9.
Lets's calculate GCF of 972,639
3 | 972, 639 |
3 | 324, 213 |
108, 71 |
∴ So the GCF of the given numbers is 3 x 3 = 9
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 639
:1,3,9,71,213,639
Greatest Common Factor
We found the factors 972,639 . The biggest common factor number is the GCF number.
So the greatest common factor 972,639 is 9.
Lets's calculate LCM of 774,138
2 | 774, 138 |
3 | 387, 69 |
129, 23 |
∴ So the LCM of the given numbers is 2 x 3 x 129 x 23 = 17802
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 9/17802
Therefore, the GCF of Fractions 972/774,639/138 is 9/17802
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 774,138 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(774,138) = 6
common factors(in case of two or more numbers have common factors) = 1
GCF(774,138) x common factors =6 x 1 = 6
LCM(774,138) = ( 774 × 138 ) / 6
LCM(774,138) = 106812 / 6
LCM(774,138) = 17802
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 972,639?
The HCF of 972,639 is 9
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 972/774, 639/138?
Answer: GCF of Numerators as per given numbers 972/774, 639/138 is
GCF of Numerators i.e. for 972,639 is 9
LCM of denominators i.e. for 774,138 is 17802.
Thus, GCF of Fractions is 9/17802.Finally, GCF of Fractions for 972/774, 639/138 is 9/17802.