Use our free GCF of Fractions Calculator tool to compute the GCF of 798/165, 882/682 i.e 42/10230 easily. The following is the detailed procedure to determine the greatest common factor of fractions 798/165, 882/682.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 798/165,882/682
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 798/165,882/682, numerators are 798,882
Denominators are 165,682
The GCF of 798,882 is 42 .
LCM of 165,682 is 10230.
The greatest common factor of 798/165,882/682 = [GCF of 798,882]/[LCM of 165,682]= 42/10230
Therefore, the GCF of 798/165,882/682 is 42/10230.
To find the highest common factor of 798,882, we have to find the factors of both numbers and list the highest common factor.
The factors of 798 are 1, 2, 3, 6, 7, 14, 19, 21, 38, 42, 57, 114, 133, 266, 399, 798
The factors of 882 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 49, 63, 98, 126, 147, 294, 441, 882
The HCF of 798,882 is 42.
Lets's calculate GCF of 798,882
2 | 798, 882 |
3 | 399, 441 |
7 | 133, 147 |
19, 21 |
∴ So the GCF of the given numbers is 2 x 3 x 7 = 42
Now, list down the factors of 798
:1,2,3,6,7,14,19,21,38,42,57,114,133,266,399,798
Now, list down the factors of 882
:1,2,3,6,7,9,14,18,21,42,49,63,98,126,147,294,441,882
Greatest Common Factor
We found the factors 798,882 . The biggest common factor number is the GCF number.
So the greatest common factor 798,882 is 42.
Lets's calculate LCM of 165,682
11 | 165, 682 |
15, 62 |
∴ So the LCM of the given numbers is 11 x 15 x 62 = 10230
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 42/10230
Therefore, the GCF of Fractions 798/165,882/682 is 42/10230
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 165,682 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(165,682) = 11
common factors(in case of two or more numbers have common factors) = 1
GCF(165,682) x common factors =11 x 1 = 11
LCM(165,682) = ( 165 × 682 ) / 11
LCM(165,682) = 112530 / 11
LCM(165,682) = 10230
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 798,882?
The HCF of 798,882 is 42
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 798/165, 882/682?
Answer: GCF of Numerators as per given numbers 798/165, 882/682 is
GCF of Numerators i.e. for 798,882 is 42
LCM of denominators i.e. for 165,682 is 10230.
Thus, GCF of Fractions is 42/10230.Finally, GCF of Fractions for 798/165, 882/682 is 42/10230.