Use our free GCF of Fractions Calculator tool to compute the GCF of 762/266, 681/308 i.e 3/5852 easily. The following is the detailed procedure to determine the greatest common factor of fractions 762/266, 681/308.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 762/266,681/308
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 762/266,681/308, numerators are 762,681
Denominators are 266,308
The GCF of 762,681 is 3 .
LCM of 266,308 is 5852.
The greatest common factor of 762/266,681/308 = [GCF of 762,681]/[LCM of 266,308]= 3/5852
Therefore, the GCF of 762/266,681/308 is 3/5852.
To find the highest common factor of 762,681, we have to find the factors of both numbers and list the highest common factor.
The factors of 762 are 1, 2, 3, 6, 127, 254, 381, 762
The factors of 681 are 1, 3, 227, 681
The HCF of 762,681 is 3.
Lets's calculate GCF of 762,681
3 | 762, 681 |
254, 227 |
∴ So the GCF of the given numbers is 3 = 3
Now, list down the factors of 762
:1,2,3,6,127,254,381,762
Now, list down the factors of 681
:1,3,227,681
Greatest Common Factor
We found the factors 762,681 . The biggest common factor number is the GCF number.
So the greatest common factor 762,681 is 3.
Lets's calculate LCM of 266,308
2 | 266, 308 |
7 | 133, 154 |
19, 22 |
∴ So the LCM of the given numbers is 2 x 7 x 19 x 22 = 5852
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/5852
Therefore, the GCF of Fractions 762/266,681/308 is 3/5852
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 266,308 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(266,308) = 14
common factors(in case of two or more numbers have common factors) = 1
GCF(266,308) x common factors =14 x 1 = 14
LCM(266,308) = ( 266 × 308 ) / 14
LCM(266,308) = 81928 / 14
LCM(266,308) = 5852
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 762,681?
The HCF of 762,681 is 3
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 762/266, 681/308?
Answer: GCF of Numerators as per given numbers 762/266, 681/308 is
GCF of Numerators i.e. for 762,681 is 3
LCM of denominators i.e. for 266,308 is 5852.
Thus, GCF of Fractions is 3/5852.Finally, GCF of Fractions for 762/266, 681/308 is 3/5852.