GCF of 30/15, 370/10, 560/369
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 30/15, 370/10, 560/369 i.e 10/3690 easily. The following is the detailed procedure to determine the greatest common factor of fractions 30/15, 370/10, 560/369.
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 30/15,370/10,560/369?
Given fractions are 30/15,370/10,560/369
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 30/15,370/10,560/369, numerators are 30,370,560
Denominators are 15,10,369
The GCF of 30,370,560 is 10 .
LCM of 15,10,369 is 3690.
The greatest common factor of 30/15,370/10,560/369 = [GCF of 30,370,560]/[LCM of 15,10,369]= 10/3690
Therefore, the GCF of 30/15,370/10,560/369 is 10/3690.
To find the highest common factor of 30,370,560, we have to find the factors of both numbers and list the highest common factor.
The factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30
The factors of 370 are 1, 2, 5, 10, 37, 74, 185, 370
The factors of 560 are 1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 28, 35, 40, 56, 70, 80, 112, 140, 280, 560
The HCF of 30,370,560 is 10.
Lets's calculate GCF of 30,370,560
| 2 | 30, 370, 560 |
| 5 | 15, 185, 280 |
| 3, 37, 56 |
∴ So the GCF of the given numbers is 2 x 5 = 10
Greatest Common Factor of 30,370,560 By Matching Biggest Common Factor Method
Now, list down the factors of 30
:1,2,3,5,6,10,15,30
Now, list down the factors of 370
:1,2,5,10,37,74,185,370
Now, list down the factors of 560
:1,2,4,5,7,8,10,14,16,20,28,35,40,56,70,80,112,140,280,560
Greatest Common Factor
We found the factors 30,370,560 . The biggest common factor number is the GCF number.
So the greatest common factor 30,370,560 is 10.
Lets's calculate LCM of 15,10,369
| 3 | 15, 10, 369 |
| 5 | 5, 10, 123 |
| 1, 2, 123 |
∴ So the LCM of the given numbers is 3 x 5 x 1 x 2 x 123 = 3690
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 10/3690
Therefore, the GCF of Fractions 30/15,370/10,560/369 is 10/3690
Least Common Multiple of 15,10,369 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 15,10,369 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(15,10,369) = 1
common factors(in case of two or more numbers have common factors) = 15
GCF(15,10,369) x common factors =1 x 15 = 15
LCM(15,10,369) = ( 15 × 10 × 369 ) / 15
LCM(15,10,369) = 55350 / 15
LCM(15,10,369) = 3690
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FAQs on GCF of Fractions of 30/15, 370/10, 560/369
1. What is the HCF of 30,370,560?
The HCF of 30,370,560 is 10
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 30/15, 370/10, 560/369?
Answer: GCF of Numerators as per given numbers 30/15, 370/10, 560/369 is
GCF of Numerators i.e. for 30,370,560 is 10
LCM of denominators i.e. for 15,10,369 is 3690.
Thus, GCF of Fractions is 10/3690.Finally, GCF of Fractions for 30/15, 370/10, 560/369 is 10/3690.