Use our free GCF of Fractions Calculator tool to compute the GCF of 705/890, 138/930 i.e 3/82770 easily. The following is the detailed procedure to determine the greatest common factor of fractions 705/890, 138/930.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 705/890,138/930
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 705/890,138/930, numerators are 705,138
Denominators are 890,930
The GCF of 705,138 is 3 .
LCM of 890,930 is 82770.
The greatest common factor of 705/890,138/930 = [GCF of 705,138]/[LCM of 890,930]= 3/82770
Therefore, the GCF of 705/890,138/930 is 3/82770.
To find the highest common factor of 705,138, we have to find the factors of both numbers and list the highest common factor.
The factors of 705 are 1, 3, 5, 15, 47, 141, 235, 705
The factors of 138 are 1, 2, 3, 6, 23, 46, 69, 138
The HCF of 705,138 is 3.
Lets's calculate GCF of 705,138
3 | 705, 138 |
235, 46 |
∴ So the GCF of the given numbers is 3 = 3
Now, list down the factors of 705
:1,3,5,15,47,141,235,705
Now, list down the factors of 138
:1,2,3,6,23,46,69,138
Greatest Common Factor
We found the factors 705,138 . The biggest common factor number is the GCF number.
So the greatest common factor 705,138 is 3.
Lets's calculate LCM of 890,930
2 | 890, 930 |
5 | 445, 465 |
89, 93 |
∴ So the LCM of the given numbers is 2 x 5 x 89 x 93 = 82770
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/82770
Therefore, the GCF of Fractions 705/890,138/930 is 3/82770
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 890,930 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(890,930) = 10
common factors(in case of two or more numbers have common factors) = 1
GCF(890,930) x common factors =10 x 1 = 10
LCM(890,930) = ( 890 × 930 ) / 10
LCM(890,930) = 827700 / 10
LCM(890,930) = 82770
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 705,138?
The HCF of 705,138 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 705/890, 138/930?
Answer: GCF of Numerators as per given numbers 705/890, 138/930 is
GCF of Numerators i.e. for 705,138 is 3
LCM of denominators i.e. for 890,930 is 82770.
Thus, GCF of Fractions is 3/82770.Finally, GCF of Fractions for 705/890, 138/930 is 3/82770.