Use our free GCF of Fractions Calculator tool to compute the GCF of 678/974, 420/709 i.e 6/690566 easily. The following is the detailed procedure to determine the greatest common factor of fractions 678/974, 420/709.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 678/974,420/709
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 678/974,420/709, numerators are 678,420
Denominators are 974,709
The GCF of 678,420 is 6 .
LCM of 974,709 is 690566.
The greatest common factor of 678/974,420/709 = [GCF of 678,420]/[LCM of 974,709]= 6/690566
Therefore, the GCF of 678/974,420/709 is 6/690566.
To find the highest common factor of 678,420, we have to find the factors of both numbers and list the highest common factor.
The factors of 678 are 1, 2, 3, 6, 113, 226, 339, 678
The factors of 420 are 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, 420
The HCF of 678,420 is 6.
Lets's calculate GCF of 678,420
2 | 678, 420 |
3 | 339, 210 |
113, 70 |
∴ So the GCF of the given numbers is 2 x 3 = 6
Now, list down the factors of 678
:1,2,3,6,113,226,339,678
Now, list down the factors of 420
:1,2,3,4,5,6,7,10,12,14,15,20,21,28,30,35,42,60,70,84,105,140,210,420
Greatest Common Factor
We found the factors 678,420 . The biggest common factor number is the GCF number.
So the greatest common factor 678,420 is 6.
Lets's calculate LCM of 974,709
Given numbers has no common factors except 1. So, there LCM is their product i.e 690566
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/690566
Therefore, the GCF of Fractions 678/974,420/709 is 6/690566
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 974,709 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(974,709) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(974,709) x common factors =1 x 1 = 1
LCM(974,709) = ( 974 × 709 ) / 1
LCM(974,709) = 690566 / 1
LCM(974,709) = 690566
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 678,420?
The HCF of 678,420 is 6
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 678/974, 420/709?
Answer: GCF of Numerators as per given numbers 678/974, 420/709 is
GCF of Numerators i.e. for 678,420 is 6
LCM of denominators i.e. for 974,709 is 690566.
Thus, GCF of Fractions is 6/690566.Finally, GCF of Fractions for 678/974, 420/709 is 6/690566.