GCF of 3/68, 2/69, 8/27, 45/360
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 3/68, 2/69, 8/27, 45/360 i.e 1/422280 easily. The following is the detailed procedure to determine the greatest common factor of fractions 3/68, 2/69, 8/27, 45/360.
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 3/68,2/69,8/27,45/360?
Given fractions are 3/68,2/69,8/27,45/360
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 3/68,2/69,8/27,45/360, numerators are 3,2,8,45
Denominators are 68,69,27,360
The GCF of 3,2,8,45 is 1 .
LCM of 68,69,27,360 is 422280.
The greatest common factor of 3/68,2/69,8/27,45/360 = [GCF of 3,2,8,45]/[LCM of 68,69,27,360]= 1/422280
Therefore, the GCF of 3/68,2/69,8/27,45/360 is 1/422280.
To find the highest common factor of 3,2,8,45, we have to find the factors of both numbers and list the highest common factor.
The factors of 3 are 1, 3
The factors of 2 are 1, 2
The factors of 8 are 1, 2, 4, 8
The factors of 45 are 1, 3, 5, 9, 15, 45
The HCF of 3,2,8,45 is 1.
Lets's calculate GCF of 3,2,8,45
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 3,2,8,45 By Matching Biggest Common Factor Method
Now, list down the factors of 3
:1,3
Now, list down the factors of 2
:1,2
Now, list down the factors of 8
:1,2,4,8
Now, list down the factors of 45
:1,3,5,9,15,45
Greatest Common Factor
We found the factors 3,2,8,45 . The biggest common factor number is the GCF number.
So the greatest common factor 3,2,8,45 is 1.
Lets's calculate LCM of 68,69,27,360
| 2 | 68, 69, 27, 360 |
| 2 | 34, 69, 27, 180 |
| 3 | 17, 69, 27, 90 |
| 3 | 17, 23, 9, 30 |
| 17, 23, 3, 10 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 3 x 17 x 23 x 3 x 10 = 422280
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/422280
Therefore, the GCF of Fractions 3/68,2/69,8/27,45/360 is 1/422280
Least Common Multiple of 68,69,27,360 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 68,69,27,360 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(68,69,27,360) = 1
common factors(in case of two or more numbers have common factors) = 108
GCF(68,69,27,360) x common factors =1 x 108 = 108
LCM(68,69,27,360) = ( 68 × 69 × 27 × 360 ) / 108
LCM(68,69,27,360) = 45606240 / 108
LCM(68,69,27,360) = 422280
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FAQs on GCF of Fractions of 3/68, 2/69, 8/27, 45/360
1. What is the HCF of 3,2,8,45?
The HCF of 3,2,8,45 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 3/68, 2/69, 8/27, 45/360?
Answer: GCF of Numerators as per given numbers 3/68, 2/69, 8/27, 45/360 is
GCF of Numerators i.e. for 3,2,8,45 is 1
LCM of denominators i.e. for 68,69,27,360 is 422280.
Thus, GCF of Fractions is 1/422280.Finally, GCF of Fractions for 3/68, 2/69, 8/27, 45/360 is 1/422280.