Use our free GCF of Fractions Calculator tool to compute the GCF of 688/670, 542/472 i.e 2/158120 easily. The following is the detailed procedure to determine the greatest common factor of fractions 688/670, 542/472.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 688/670,542/472
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 688/670,542/472, numerators are 688,542
Denominators are 670,472
The GCF of 688,542 is 2 .
LCM of 670,472 is 158120.
The greatest common factor of 688/670,542/472 = [GCF of 688,542]/[LCM of 670,472]= 2/158120
Therefore, the GCF of 688/670,542/472 is 2/158120.
To find the highest common factor of 688,542, we have to find the factors of both numbers and list the highest common factor.
The factors of 688 are 1, 2, 4, 8, 16, 43, 86, 172, 344, 688
The factors of 542 are 1, 2, 271, 542
The HCF of 688,542 is 2.
Lets's calculate GCF of 688,542
2 | 688, 542 |
344, 271 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 688
:1,2,4,8,16,43,86,172,344,688
Now, list down the factors of 542
:1,2,271,542
Greatest Common Factor
We found the factors 688,542 . The biggest common factor number is the GCF number.
So the greatest common factor 688,542 is 2.
Lets's calculate LCM of 670,472
2 | 670, 472 |
335, 236 |
∴ So the LCM of the given numbers is 2 x 335 x 236 = 158120
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/158120
Therefore, the GCF of Fractions 688/670,542/472 is 2/158120
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 670,472 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(670,472) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(670,472) x common factors =2 x 1 = 2
LCM(670,472) = ( 670 × 472 ) / 2
LCM(670,472) = 316240 / 2
LCM(670,472) = 158120
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 688,542?
The HCF of 688,542 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 688/670, 542/472?
Answer: GCF of Numerators as per given numbers 688/670, 542/472 is
GCF of Numerators i.e. for 688,542 is 2
LCM of denominators i.e. for 670,472 is 158120.
Thus, GCF of Fractions is 2/158120.Finally, GCF of Fractions for 688/670, 542/472 is 2/158120.