GCF of 810/13, 840/715
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 810/13, 840/715 i.e 30/715 easily. The following is the detailed procedure to determine the greatest common factor of fractions 810/13, 840/715.
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 810/13,840/715?
Given fractions are 810/13,840/715
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 810/13,840/715, numerators are 810,840
Denominators are 13,715
The GCF of 810,840 is 30 .
LCM of 13,715 is 715.
The greatest common factor of 810/13,840/715 = [GCF of 810,840]/[LCM of 13,715]= 30/715
Therefore, the GCF of 810/13,840/715 is 30/715.
To find the highest common factor of 810,840, we have to find the factors of both numbers and list the highest common factor.
The factors of 810 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 81, 90, 135, 162, 270, 405, 810
The factors of 840 are 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24, 28, 30, 35, 40, 42, 56, 60, 70, 84, 105, 120, 140, 168, 210, 280, 420, 840
The HCF of 810,840 is 30.
Lets's calculate GCF of 810,840
| 2 | 810, 840 |
| 3 | 405, 420 |
| 5 | 135, 140 |
| 27, 28 |
∴ So the GCF of the given numbers is 2 x 3 x 5 = 30
Greatest Common Factor of 810,840 By Matching Biggest Common Factor Method
Now, list down the factors of 810
:1,2,3,5,6,9,10,15,18,27,30,45,54,81,90,135,162,270,405,810
Now, list down the factors of 840
:1,2,3,4,5,6,7,8,10,12,14,15,20,21,24,28,30,35,40,42,56,60,70,84,105,120,140,168,210,280,420,840
Greatest Common Factor
We found the factors 810,840 . The biggest common factor number is the GCF number.
So the greatest common factor 810,840 is 30.
Lets's calculate LCM of 13,715
| 13 | 13, 715 |
| 1, 55 |
∴ So the LCM of the given numbers is 13 x 1 x 55 = 715
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 30/715
Therefore, the GCF of Fractions 810/13,840/715 is 30/715
Least Common Multiple of 13,715 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 13,715 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(13,715) = 13
common factors(in case of two or more numbers have common factors) = 1
GCF(13,715) x common factors =13 x 1 = 13
LCM(13,715) = ( 13 × 715 ) / 13
LCM(13,715) = 9295 / 13
LCM(13,715) = 715
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FAQs on GCF of Fractions of 810/13, 840/715
1. What is the HCF of 810,840?
The HCF of 810,840 is 30
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 810/13, 840/715?
Answer: GCF of Numerators as per given numbers 810/13, 840/715 is
GCF of Numerators i.e. for 810,840 is 30
LCM of denominators i.e. for 13,715 is 715.
Thus, GCF of Fractions is 30/715.Finally, GCF of Fractions for 810/13, 840/715 is 30/715.