Use our free GCF of Fractions Calculator tool to compute the GCF of 954/714, 657/672 i.e 9/11424 easily. The following is the detailed procedure to determine the greatest common factor of fractions 954/714, 657/672.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 954/714,657/672
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 954/714,657/672, numerators are 954,657
Denominators are 714,672
The GCF of 954,657 is 9 .
LCM of 714,672 is 11424.
The greatest common factor of 954/714,657/672 = [GCF of 954,657]/[LCM of 714,672]= 9/11424
Therefore, the GCF of 954/714,657/672 is 9/11424.
To find the highest common factor of 954,657, we have to find the factors of both numbers and list the highest common factor.
The factors of 954 are 1, 2, 3, 6, 9, 18, 53, 106, 159, 318, 477, 954
The factors of 657 are 1, 3, 9, 73, 219, 657
The HCF of 954,657 is 9.
Lets's calculate GCF of 954,657
3 | 954, 657 |
3 | 318, 219 |
106, 73 |
∴ So the GCF of the given numbers is 3 x 3 = 9
Now, list down the factors of 954
:1,2,3,6,9,18,53,106,159,318,477,954
Now, list down the factors of 657
:1,3,9,73,219,657
Greatest Common Factor
We found the factors 954,657 . The biggest common factor number is the GCF number.
So the greatest common factor 954,657 is 9.
Lets's calculate LCM of 714,672
2 | 714, 672 |
3 | 357, 336 |
7 | 119, 112 |
17, 16 |
∴ So the LCM of the given numbers is 2 x 3 x 7 x 17 x 16 = 11424
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 9/11424
Therefore, the GCF of Fractions 954/714,657/672 is 9/11424
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 714,672 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(714,672) = 42
common factors(in case of two or more numbers have common factors) = 1
GCF(714,672) x common factors =42 x 1 = 42
LCM(714,672) = ( 714 × 672 ) / 42
LCM(714,672) = 479808 / 42
LCM(714,672) = 11424
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 954,657?
The HCF of 954,657 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 954/714, 657/672?
Answer: GCF of Numerators as per given numbers 954/714, 657/672 is
GCF of Numerators i.e. for 954,657 is 9
LCM of denominators i.e. for 714,672 is 11424.
Thus, GCF of Fractions is 9/11424.Finally, GCF of Fractions for 954/714, 657/672 is 9/11424.