Use our free GCF of Fractions Calculator tool to compute the GCF of 69/38, 504/42, 653/305 i.e 1/243390 easily. The following is the detailed procedure to determine the greatest common factor of fractions 69/38, 504/42, 653/305.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 69/38,504/42,653/305
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 69/38,504/42,653/305, numerators are 69,504,653
Denominators are 38,42,305
The GCF of 69,504,653 is 1 .
LCM of 38,42,305 is 243390.
The greatest common factor of 69/38,504/42,653/305 = [GCF of 69,504,653]/[LCM of 38,42,305]= 1/243390
Therefore, the GCF of 69/38,504/42,653/305 is 1/243390.
To find the highest common factor of 69,504,653, we have to find the factors of both numbers and list the highest common factor.
The factors of 69 are 1, 3, 23, 69
The factors of 504 are 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 21, 24, 28, 36, 42, 56, 63, 72, 84, 126, 168, 252, 504
The factors of 653 are 1, 653
The HCF of 69,504,653 is 1.
Lets's calculate GCF of 69,504,653
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 69
:1,3,23,69
Now, list down the factors of 504
:1,2,3,4,6,7,8,9,12,14,18,21,24,28,36,42,56,63,72,84,126,168,252,504
Now, list down the factors of 653
:1,653
Greatest Common Factor
We found the factors 69,504,653 . The biggest common factor number is the GCF number.
So the greatest common factor 69,504,653 is 1.
Lets's calculate LCM of 38,42,305
2 | 38, 42, 305 |
19, 21, 305 |
∴ So the LCM of the given numbers is 2 x 19 x 21 x 305 = 243390
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/243390
Therefore, the GCF of Fractions 69/38,504/42,653/305 is 1/243390
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 38,42,305 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(38,42,305) = 1
common factors(in case of two or more numbers have common factors) = 2
GCF(38,42,305) x common factors =1 x 2 = 2
LCM(38,42,305) = ( 38 × 42 × 305 ) / 2
LCM(38,42,305) = 486780 / 2
LCM(38,42,305) = 243390
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 69,504,653?
The HCF of 69,504,653 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 69/38, 504/42, 653/305?
Answer: GCF of Numerators as per given numbers 69/38, 504/42, 653/305 is
GCF of Numerators i.e. for 69,504,653 is 1
LCM of denominators i.e. for 38,42,305 is 243390.
Thus, GCF of Fractions is 1/243390.Finally, GCF of Fractions for 69/38, 504/42, 653/305 is 1/243390.