Use our free GCF of Fractions Calculator tool to compute the GCF of 35/288, 84/172, 416/107 i.e 1/1325088 easily. The following is the detailed procedure to determine the greatest common factor of fractions 35/288, 84/172, 416/107.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 35/288,84/172,416/107
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 35/288,84/172,416/107, numerators are 35,84,416
Denominators are 288,172,107
The GCF of 35,84,416 is 1 .
LCM of 288,172,107 is 1325088.
The greatest common factor of 35/288,84/172,416/107 = [GCF of 35,84,416]/[LCM of 288,172,107]= 1/1325088
Therefore, the GCF of 35/288,84/172,416/107 is 1/1325088.
To find the highest common factor of 35,84,416, we have to find the factors of both numbers and list the highest common factor.
The factors of 35 are 1, 5, 7, 35
The factors of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
The factors of 416 are 1, 2, 4, 8, 13, 16, 26, 32, 52, 104, 208, 416
The HCF of 35,84,416 is 1.
Lets's calculate GCF of 35,84,416
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 35
:1,5,7,35
Now, list down the factors of 84
:1,2,3,4,6,7,12,14,21,28,42,84
Now, list down the factors of 416
:1,2,4,8,13,16,26,32,52,104,208,416
Greatest Common Factor
We found the factors 35,84,416 . The biggest common factor number is the GCF number.
So the greatest common factor 35,84,416 is 1.
Lets's calculate LCM of 288,172,107
2 | 288, 172, 107 |
2 | 144, 86, 107 |
72, 43, 107 |
∴ So the LCM of the given numbers is 2 x 2 x 72 x 43 x 107 = 1325088
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/1325088
Therefore, the GCF of Fractions 35/288,84/172,416/107 is 1/1325088
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 288,172,107 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(288,172,107) = 1
common factors(in case of two or more numbers have common factors) = 4
GCF(288,172,107) x common factors =1 x 4 = 4
LCM(288,172,107) = ( 288 × 172 × 107 ) / 4
LCM(288,172,107) = 5300352 / 4
LCM(288,172,107) = 1325088
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 35,84,416?
The HCF of 35,84,416 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 35/288, 84/172, 416/107?
Answer: GCF of Numerators as per given numbers 35/288, 84/172, 416/107 is
GCF of Numerators i.e. for 35,84,416 is 1
LCM of denominators i.e. for 288,172,107 is 1325088.
Thus, GCF of Fractions is 1/1325088.Finally, GCF of Fractions for 35/288, 84/172, 416/107 is 1/1325088.