Use our free GCF of Fractions Calculator tool to compute the GCF of 7/84, 10/70, 71/76, 26/32 i.e 1/63840 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7/84, 10/70, 71/76, 26/32.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 7/84,10/70,71/76,26/32
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 7/84,10/70,71/76,26/32, numerators are 7,10,71,26
Denominators are 84,70,76,32
The GCF of 7,10,71,26 is 1 .
LCM of 84,70,76,32 is 63840.
The greatest common factor of 7/84,10/70,71/76,26/32 = [GCF of 7,10,71,26]/[LCM of 84,70,76,32]= 1/63840
Therefore, the GCF of 7/84,10/70,71/76,26/32 is 1/63840.
To find the highest common factor of 7,10,71,26, we have to find the factors of both numbers and list the highest common factor.
The factors of 7 are 1, 7
The factors of 10 are 1, 2, 5, 10
The factors of 71 are 1, 71
The factors of 26 are 1, 2, 13, 26
The HCF of 7,10,71,26 is 1.
Lets's calculate GCF of 7,10,71,26
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 7
:1,7
Now, list down the factors of 10
:1,2,5,10
Now, list down the factors of 71
:1,71
Now, list down the factors of 26
:1,2,13,26
Greatest Common Factor
We found the factors 7,10,71,26 . The biggest common factor number is the GCF number.
So the greatest common factor 7,10,71,26 is 1.
Lets's calculate LCM of 84,70,76,32
2 | 84, 70, 76, 32 |
2 | 42, 35, 38, 16 |
7 | 21, 35, 19, 8 |
3, 5, 19, 8 |
∴ So the LCM of the given numbers is 2 x 2 x 7 x 3 x 5 x 19 x 8 = 63840
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/63840
Therefore, the GCF of Fractions 7/84,10/70,71/76,26/32 is 1/63840
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 84,70,76,32 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(84,70,76,32) = 2
common factors(in case of two or more numbers have common factors) = 112
GCF(84,70,76,32) x common factors =2 x 112 = 224
LCM(84,70,76,32) = ( 84 × 70 × 76 × 32 ) / 224
LCM(84,70,76,32) = 14300160 / 224
LCM(84,70,76,32) = 63840
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 7,10,71,26?
The HCF of 7,10,71,26 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 7/84, 10/70, 71/76, 26/32?
Answer: GCF of Numerators as per given numbers 7/84, 10/70, 71/76, 26/32 is
GCF of Numerators i.e. for 7,10,71,26 is 1
LCM of denominators i.e. for 84,70,76,32 is 63840.
Thus, GCF of Fractions is 1/63840.Finally, GCF of Fractions for 7/84, 10/70, 71/76, 26/32 is 1/63840.