Use our free GCF of Fractions Calculator tool to compute the GCF of 28/686, 45/710, 562/742 i.e 1/12907090 easily. The following is the detailed procedure to determine the greatest common factor of fractions 28/686, 45/710, 562/742.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 28/686,45/710,562/742
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 28/686,45/710,562/742, numerators are 28,45,562
Denominators are 686,710,742
The GCF of 28,45,562 is 1 .
LCM of 686,710,742 is 12907090.
The greatest common factor of 28/686,45/710,562/742 = [GCF of 28,45,562]/[LCM of 686,710,742]= 1/12907090
Therefore, the GCF of 28/686,45/710,562/742 is 1/12907090.
To find the highest common factor of 28,45,562, we have to find the factors of both numbers and list the highest common factor.
The factors of 28 are 1, 2, 4, 7, 14, 28
The factors of 45 are 1, 3, 5, 9, 15, 45
The factors of 562 are 1, 2, 281, 562
The HCF of 28,45,562 is 1.
Lets's calculate GCF of 28,45,562
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 28
:1,2,4,7,14,28
Now, list down the factors of 45
:1,3,5,9,15,45
Now, list down the factors of 562
:1,2,281,562
Greatest Common Factor
We found the factors 28,45,562 . The biggest common factor number is the GCF number.
So the greatest common factor 28,45,562 is 1.
Lets's calculate LCM of 686,710,742
2 | 686, 710, 742 |
7 | 343, 355, 371 |
49, 355, 53 |
∴ So the LCM of the given numbers is 2 x 7 x 49 x 355 x 53 = 12907090
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/12907090
Therefore, the GCF of Fractions 28/686,45/710,562/742 is 1/12907090
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 686,710,742 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(686,710,742) = 2
common factors(in case of two or more numbers have common factors) = 14
GCF(686,710,742) x common factors =2 x 14 = 28
LCM(686,710,742) = ( 686 × 710 × 742 ) / 28
LCM(686,710,742) = 361398520 / 28
LCM(686,710,742) = 12907090
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 28,45,562?
The HCF of 28,45,562 is 1
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 28/686, 45/710, 562/742?
Answer: GCF of Numerators as per given numbers 28/686, 45/710, 562/742 is
GCF of Numerators i.e. for 28,45,562 is 1
LCM of denominators i.e. for 686,710,742 is 12907090.
Thus, GCF of Fractions is 1/12907090.Finally, GCF of Fractions for 28/686, 45/710, 562/742 is 1/12907090.