GCF of 8/36, 71/39, 68/132, 362/135
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 8/36, 71/39, 68/132, 362/135 i.e 1/77220 easily. The following is the detailed procedure to determine the greatest common factor of fractions 8/36, 71/39, 68/132, 362/135.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
What is the GCF of 8/36,71/39,68/132,362/135?
Given fractions are 8/36,71/39,68/132,362/135
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 8/36,71/39,68/132,362/135, numerators are 8,71,68,362
Denominators are 36,39,132,135
The GCF of 8,71,68,362 is 1 .
LCM of 36,39,132,135 is 77220.
The greatest common factor of 8/36,71/39,68/132,362/135 = [GCF of 8,71,68,362]/[LCM of 36,39,132,135]= 1/77220
Therefore, the GCF of 8/36,71/39,68/132,362/135 is 1/77220.
To find the highest common factor of 8,71,68,362, we have to find the factors of both numbers and list the highest common factor.
The factors of 8 are 1, 2, 4, 8
The factors of 71 are 1, 71
The factors of 68 are 1, 2, 4, 17, 34, 68
The factors of 362 are 1, 2, 181, 362
The HCF of 8,71,68,362 is 1.
Lets's calculate GCF of 8,71,68,362
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 8,71,68,362 By Matching Biggest Common Factor Method
Now, list down the factors of 8
:1,2,4,8
Now, list down the factors of 71
:1,71
Now, list down the factors of 68
:1,2,4,17,34,68
Now, list down the factors of 362
:1,2,181,362
Greatest Common Factor
We found the factors 8,71,68,362 . The biggest common factor number is the GCF number.
So the greatest common factor 8,71,68,362 is 1.
Lets's calculate LCM of 36,39,132,135
| 2 | 36, 39, 132, 135 |
| 2 | 18, 39, 66, 135 |
| 3 | 9, 39, 33, 135 |
| 3 | 3, 13, 11, 45 |
| 1, 13, 11, 15 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 3 x 1 x 13 x 11 x 15 = 77220
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/77220
Therefore, the GCF of Fractions 8/36,71/39,68/132,362/135 is 1/77220
Least Common Multiple of 36,39,132,135 with GCF Formula
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 36,39,132,135 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(36,39,132,135) = 3
common factors(in case of two or more numbers have common factors) = 108
GCF(36,39,132,135) x common factors =3 x 108 = 324
LCM(36,39,132,135) = ( 36 × 39 × 132 × 135 ) / 324
LCM(36,39,132,135) = 25019280 / 324
LCM(36,39,132,135) = 77220
GCF of Fractions Calculation Examples
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FAQs on GCF of Fractions of 8/36, 71/39, 68/132, 362/135
1. What is the HCF of 8,71,68,362?
The HCF of 8,71,68,362 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 8/36, 71/39, 68/132, 362/135?
Answer: GCF of Numerators as per given numbers 8/36, 71/39, 68/132, 362/135 is
GCF of Numerators i.e. for 8,71,68,362 is 1
LCM of denominators i.e. for 36,39,132,135 is 77220.
Thus, GCF of Fractions is 1/77220.Finally, GCF of Fractions for 8/36, 71/39, 68/132, 362/135 is 1/77220.