Use our free GCF of Fractions Calculator tool to compute the GCF of 84/414, 70/946 i.e 14/195822 easily. The following is the detailed procedure to determine the greatest common factor of fractions 84/414, 70/946.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 84/414,70/946
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 84/414,70/946, numerators are 84,70
Denominators are 414,946
The GCF of 84,70 is 14 .
LCM of 414,946 is 195822.
The greatest common factor of 84/414,70/946 = [GCF of 84,70]/[LCM of 414,946]= 14/195822
Therefore, the GCF of 84/414,70/946 is 14/195822.
To find the highest common factor of 84,70, we have to find the factors of both numbers and list the highest common factor.
The factors of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
The factors of 70 are 1, 2, 5, 7, 10, 14, 35, 70
The HCF of 84,70 is 14.
Lets's calculate GCF of 84,70
2 | 84, 70 |
7 | 42, 35 |
6, 5 |
∴ So the GCF of the given numbers is 2 x 7 = 14
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 70
:1,2,5,7,10,14,35,70
Greatest Common Factor
We found the factors 84,70 . The biggest common factor number is the GCF number.
So the greatest common factor 84,70 is 14.
Lets's calculate LCM of 414,946
2 | 414, 946 |
207, 473 |
∴ So the LCM of the given numbers is 2 x 207 x 473 = 195822
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 14/195822
Therefore, the GCF of Fractions 84/414,70/946 is 14/195822
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 414,946 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(414,946) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(414,946) x common factors =2 x 1 = 2
LCM(414,946) = ( 414 × 946 ) / 2
LCM(414,946) = 391644 / 2
LCM(414,946) = 195822
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 84,70?
The HCF of 84,70 is 14
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 84/414, 70/946?
Answer: GCF of Numerators as per given numbers 84/414, 70/946 is
GCF of Numerators i.e. for 84,70 is 14
LCM of denominators i.e. for 414,946 is 195822.
Thus, GCF of Fractions is 14/195822.Finally, GCF of Fractions for 84/414, 70/946 is 14/195822.