Use our free GCF of Fractions Calculator tool to compute the GCF of 17/702, 42/120, 407/486 i.e 1/126360 easily. The following is the detailed procedure to determine the greatest common factor of fractions 17/702, 42/120, 407/486.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 17/702,42/120,407/486
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 17/702,42/120,407/486, numerators are 17,42,407
Denominators are 702,120,486
The GCF of 17,42,407 is 1 .
LCM of 702,120,486 is 126360.
The greatest common factor of 17/702,42/120,407/486 = [GCF of 17,42,407]/[LCM of 702,120,486]= 1/126360
Therefore, the GCF of 17/702,42/120,407/486 is 1/126360.
To find the highest common factor of 17,42,407, we have to find the factors of both numbers and list the highest common factor.
The factors of 17 are 1, 17
The factors of 42 are 1, 2, 3, 6, 7, 14, 21, 42
The factors of 407 are 1, 11, 37, 407
The HCF of 17,42,407 is 1.
Lets's calculate GCF of 17,42,407
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 17
:1,17
Now, list down the factors of 42
:1,2,3,6,7,14,21,42
Now, list down the factors of 407
:1,11,37,407
Greatest Common Factor
We found the factors 17,42,407 . The biggest common factor number is the GCF number.
So the greatest common factor 17,42,407 is 1.
Lets's calculate LCM of 702,120,486
2 | 702, 120, 486 |
3 | 351, 60, 243 |
3 | 117, 20, 81 |
3 | 39, 20, 27 |
13, 20, 9 |
∴ So the LCM of the given numbers is 2 x 3 x 3 x 3 x 13 x 20 x 9 = 126360
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/126360
Therefore, the GCF of Fractions 17/702,42/120,407/486 is 1/126360
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 702,120,486 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(702,120,486) = 6
common factors(in case of two or more numbers have common factors) = 54
GCF(702,120,486) x common factors =6 x 54 = 324
LCM(702,120,486) = ( 702 × 120 × 486 ) / 324
LCM(702,120,486) = 40940640 / 324
LCM(702,120,486) = 126360
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 17,42,407?
The HCF of 17,42,407 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 17/702, 42/120, 407/486?
Answer: GCF of Numerators as per given numbers 17/702, 42/120, 407/486 is
GCF of Numerators i.e. for 17,42,407 is 1
LCM of denominators i.e. for 702,120,486 is 126360.
Thus, GCF of Fractions is 1/126360.Finally, GCF of Fractions for 17/702, 42/120, 407/486 is 1/126360.