GCF of 15/14, 69/72, 360/277
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 15/14, 69/72, 360/277 i.e 3/139608 easily. The following is the detailed procedure to determine the greatest common factor of fractions 15/14, 69/72, 360/277.
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 15/14,69/72,360/277?
Given fractions are 15/14,69/72,360/277
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 15/14,69/72,360/277, numerators are 15,69,360
Denominators are 14,72,277
The GCF of 15,69,360 is 3 .
LCM of 14,72,277 is 139608.
The greatest common factor of 15/14,69/72,360/277 = [GCF of 15,69,360]/[LCM of 14,72,277]= 3/139608
Therefore, the GCF of 15/14,69/72,360/277 is 3/139608.
To find the highest common factor of 15,69,360, we have to find the factors of both numbers and list the highest common factor.
The factors of 15 are 1, 3, 5, 15
The factors of 69 are 1, 3, 23, 69
The factors of 360 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360
The HCF of 15,69,360 is 3.
Lets's calculate GCF of 15,69,360
| 3 | 15, 69, 360 |
| 5, 23, 120 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 15,69,360 By Matching Biggest Common Factor Method
Now, list down the factors of 15
:1,3,5,15
Now, list down the factors of 69
:1,3,23,69
Now, list down the factors of 360
:1,2,3,4,5,6,8,9,10,12,15,18,20,24,30,36,40,45,60,72,90,120,180,360
Greatest Common Factor
We found the factors 15,69,360 . The biggest common factor number is the GCF number.
So the greatest common factor 15,69,360 is 3.
Lets's calculate LCM of 14,72,277
| 2 | 14, 72, 277 |
| 7, 36, 277 |
∴ So the LCM of the given numbers is 2 x 7 x 36 x 277 = 139608
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/139608
Therefore, the GCF of Fractions 15/14,69/72,360/277 is 3/139608
Least Common Multiple of 14,72,277 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 14,72,277 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(14,72,277) = 1
common factors(in case of two or more numbers have common factors) = 2
GCF(14,72,277) x common factors =1 x 2 = 2
LCM(14,72,277) = ( 14 × 72 × 277 ) / 2
LCM(14,72,277) = 279216 / 2
LCM(14,72,277) = 139608
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FAQs on GCF of Fractions of 15/14, 69/72, 360/277
1. What is the HCF of 15,69,360?
The HCF of 15,69,360 is 3
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 15/14, 69/72, 360/277?
Answer: GCF of Numerators as per given numbers 15/14, 69/72, 360/277 is
GCF of Numerators i.e. for 15,69,360 is 3
LCM of denominators i.e. for 14,72,277 is 139608.
Thus, GCF of Fractions is 3/139608.Finally, GCF of Fractions for 15/14, 69/72, 360/277 is 3/139608.