Use our free GCF of Fractions Calculator tool to compute the GCF of 784/670, 697/304 i.e 1/101840 easily. The following is the detailed procedure to determine the greatest common factor of fractions 784/670, 697/304.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 784/670,697/304
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 784/670,697/304, numerators are 784,697
Denominators are 670,304
The GCF of 784,697 is 1 .
LCM of 670,304 is 101840.
The greatest common factor of 784/670,697/304 = [GCF of 784,697]/[LCM of 670,304]= 1/101840
Therefore, the GCF of 784/670,697/304 is 1/101840.
To find the highest common factor of 784,697, we have to find the factors of both numbers and list the highest common factor.
The factors of 784 are 1, 2, 4, 7, 8, 14, 16, 28, 49, 56, 98, 112, 196, 392, 784
The factors of 697 are 1, 17, 41, 697
The HCF of 784,697 is 1.
Lets's calculate GCF of 784,697
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 784
:1,2,4,7,8,14,16,28,49,56,98,112,196,392,784
Now, list down the factors of 697
:1,17,41,697
Greatest Common Factor
We found the factors 784,697 . The biggest common factor number is the GCF number.
So the greatest common factor 784,697 is 1.
Lets's calculate LCM of 670,304
2 | 670, 304 |
335, 152 |
∴ So the LCM of the given numbers is 2 x 335 x 152 = 101840
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/101840
Therefore, the GCF of Fractions 784/670,697/304 is 1/101840
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 670,304 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(670,304) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(670,304) x common factors =2 x 1 = 2
LCM(670,304) = ( 670 × 304 ) / 2
LCM(670,304) = 203680 / 2
LCM(670,304) = 101840
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 784,697?
The HCF of 784,697 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 784/670, 697/304?
Answer: GCF of Numerators as per given numbers 784/670, 697/304 is
GCF of Numerators i.e. for 784,697 is 1
LCM of denominators i.e. for 670,304 is 101840.
Thus, GCF of Fractions is 1/101840.Finally, GCF of Fractions for 784/670, 697/304 is 1/101840.