Use our free GCF of Fractions Calculator tool to compute the GCF of 76/895, 72/170, 342/765 i.e 2/273870 easily. The following is the detailed procedure to determine the greatest common factor of fractions 76/895, 72/170, 342/765.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 76/895,72/170,342/765
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 76/895,72/170,342/765, numerators are 76,72,342
Denominators are 895,170,765
The GCF of 76,72,342 is 2 .
LCM of 895,170,765 is 273870.
The greatest common factor of 76/895,72/170,342/765 = [GCF of 76,72,342]/[LCM of 895,170,765]= 2/273870
Therefore, the GCF of 76/895,72/170,342/765 is 2/273870.
To find the highest common factor of 76,72,342, we have to find the factors of both numbers and list the highest common factor.
The factors of 76 are 1, 2, 4, 19, 38, 76
The factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
The factors of 342 are 1, 2, 3, 6, 9, 18, 19, 38, 57, 114, 171, 342
The HCF of 76,72,342 is 2.
Lets's calculate GCF of 76,72,342
2 | 76, 72, 342 |
38, 36, 171 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 76
:1,2,4,19,38,76
Now, list down the factors of 72
:1,2,3,4,6,8,9,12,18,24,36,72
Now, list down the factors of 342
:1,2,3,6,9,18,19,38,57,114,171,342
Greatest Common Factor
We found the factors 76,72,342 . The biggest common factor number is the GCF number.
So the greatest common factor 76,72,342 is 2.
Lets's calculate LCM of 895,170,765
5 | 895, 170, 765 |
17 | 179, 34, 153 |
179, 2, 9 |
∴ So the LCM of the given numbers is 5 x 17 x 179 x 2 x 9 = 273870
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/273870
Therefore, the GCF of Fractions 76/895,72/170,342/765 is 2/273870
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 895,170,765 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(895,170,765) = 5
common factors(in case of two or more numbers have common factors) = 85
GCF(895,170,765) x common factors =5 x 85 = 425
LCM(895,170,765) = ( 895 × 170 × 765 ) / 425
LCM(895,170,765) = 116394750 / 425
LCM(895,170,765) = 273870
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 76,72,342?
The HCF of 76,72,342 is 2
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 76/895, 72/170, 342/765?
Answer: GCF of Numerators as per given numbers 76/895, 72/170, 342/765 is
GCF of Numerators i.e. for 76,72,342 is 2
LCM of denominators i.e. for 895,170,765 is 273870.
Thus, GCF of Fractions is 2/273870.Finally, GCF of Fractions for 76/895, 72/170, 342/765 is 2/273870.