Use our free GCF of Fractions Calculator tool to compute the GCF of 544/406, 170/102 i.e 34/20706 easily. The following is the detailed procedure to determine the greatest common factor of fractions 544/406, 170/102.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 544/406,170/102
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 544/406,170/102, numerators are 544,170
Denominators are 406,102
The GCF of 544,170 is 34 .
LCM of 406,102 is 20706.
The greatest common factor of 544/406,170/102 = [GCF of 544,170]/[LCM of 406,102]= 34/20706
Therefore, the GCF of 544/406,170/102 is 34/20706.
To find the highest common factor of 544,170, we have to find the factors of both numbers and list the highest common factor.
The factors of 544 are 1, 2, 4, 8, 16, 17, 32, 34, 68, 136, 272, 544
The factors of 170 are 1, 2, 5, 10, 17, 34, 85, 170
The HCF of 544,170 is 34.
Lets's calculate GCF of 544,170
2 | 544, 170 |
17 | 272, 85 |
16, 5 |
∴ So the GCF of the given numbers is 2 x 17 = 34
Now, list down the factors of 544
:1,2,4,8,16,17,32,34,68,136,272,544
Now, list down the factors of 170
:1,2,5,10,17,34,85,170
Greatest Common Factor
We found the factors 544,170 . The biggest common factor number is the GCF number.
So the greatest common factor 544,170 is 34.
Lets's calculate LCM of 406,102
2 | 406, 102 |
203, 51 |
∴ So the LCM of the given numbers is 2 x 203 x 51 = 20706
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 34/20706
Therefore, the GCF of Fractions 544/406,170/102 is 34/20706
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 406,102 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(406,102) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(406,102) x common factors =2 x 1 = 2
LCM(406,102) = ( 406 × 102 ) / 2
LCM(406,102) = 41412 / 2
LCM(406,102) = 20706
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 544,170?
The HCF of 544,170 is 34
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 544/406, 170/102?
Answer: GCF of Numerators as per given numbers 544/406, 170/102 is
GCF of Numerators i.e. for 544,170 is 34
LCM of denominators i.e. for 406,102 is 20706.
Thus, GCF of Fractions is 34/20706.Finally, GCF of Fractions for 544/406, 170/102 is 34/20706.