GCF of 365/420, 1320/2814
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 365/420, 1320/2814 i.e 5/28140 easily. The following is the detailed procedure to determine the greatest common factor of fractions 365/420, 1320/2814.
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 365/420,1320/2814?
Given fractions are 365/420,1320/2814
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 365/420,1320/2814, numerators are 365,1320
Denominators are 420,2814
The GCF of 365,1320 is 5 .
LCM of 420,2814 is 28140.
The greatest common factor of 365/420,1320/2814 = [GCF of 365,1320]/[LCM of 420,2814]= 5/28140
Therefore, the GCF of 365/420,1320/2814 is 5/28140.
To find the highest common factor of 365,1320, we have to find the factors of both numbers and list the highest common factor.
The factors of 365 are 1, 5, 73, 365
The factors of 1320 are 1, 2, 3, 4, 5, 6, 8, 10, 11, 12, 15, 20, 22, 24, 30, 33, 40, 44, 55, 60, 66, 88, 110, 120, 132, 165, 220, 264, 330, 440, 660, 1320
The HCF of 365,1320 is 5.
Lets's calculate GCF of 365,1320
| 5 | 365, 1320 |
| 73, 264 |
∴ So the GCF of the given numbers is 5 = 5
Greatest Common Factor of 365,1320 By Matching Biggest Common Factor Method
Now, list down the factors of 365
:1,5,73,365
Now, list down the factors of 1320
:1,2,3,4,5,6,8,10,11,12,15,20,22,24,30,33,40,44,55,60,66,88,110,120,132,165,220,264,330,440,660,1320
Greatest Common Factor
We found the factors 365,1320 . The biggest common factor number is the GCF number.
So the greatest common factor 365,1320 is 5.
Lets's calculate LCM of 420,2814
| 2 | 420, 2814 |
| 3 | 210, 1407 |
| 7 | 70, 469 |
| 10, 67 |
∴ So the LCM of the given numbers is 2 x 3 x 7 x 10 x 67 = 28140
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 5/28140
Therefore, the GCF of Fractions 365/420,1320/2814 is 5/28140
Least Common Multiple of 420,2814 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 420,2814 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(420,2814) = 42
common factors(in case of two or more numbers have common factors) = 1
GCF(420,2814) x common factors =42 x 1 = 42
LCM(420,2814) = ( 420 × 2814 ) / 42
LCM(420,2814) = 1181880 / 42
LCM(420,2814) = 28140
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FAQs on GCF of Fractions of 365/420, 1320/2814
1. What is the HCF of 365,1320?
The HCF of 365,1320 is 5
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 365/420, 1320/2814?
Answer: GCF of Numerators as per given numbers 365/420, 1320/2814 is
GCF of Numerators i.e. for 365,1320 is 5
LCM of denominators i.e. for 420,2814 is 28140.
Thus, GCF of Fractions is 5/28140.Finally, GCF of Fractions for 365/420, 1320/2814 is 5/28140.