GCF of 5670/281, 6840/331
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 5670/281, 6840/331 i.e 90/93011 easily. The following is the detailed procedure to determine the greatest common factor of fractions 5670/281, 6840/331.
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 5670/281,6840/331?
Given fractions are 5670/281,6840/331
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 5670/281,6840/331, numerators are 5670,6840
Denominators are 281,331
The GCF of 5670,6840 is 90 .
LCM of 281,331 is 93011.
The greatest common factor of 5670/281,6840/331 = [GCF of 5670,6840]/[LCM of 281,331]= 90/93011
Therefore, the GCF of 5670/281,6840/331 is 90/93011.
To find the highest common factor of 5670,6840, we have to find the factors of both numbers and list the highest common factor.
The factors of 5670 are 1, 2, 3, 5, 6, 7, 9, 10, 14, 15, 18, 21, 27, 30, 35, 42, 45, 54, 63, 70, 81, 90, 105, 126, 135, 162, 189, 210, 270, 315, 378, 405, 567, 630, 810, 945, 1134, 1890, 2835, 5670
The factors of 6840 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 19, 20, 24, 30, 36, 38, 40, 45, 57, 60, 72, 76, 90, 95, 114, 120, 152, 171, 180, 190, 228, 285, 342, 360, 380, 456, 570, 684, 760, 855, 1140, 1368, 1710, 2280, 3420, 6840
The HCF of 5670,6840 is 90.
Lets's calculate GCF of 5670,6840
| 2 | 5670, 6840 |
| 3 | 2835, 3420 |
| 3 | 945, 1140 |
| 5 | 315, 380 |
| 63, 76 |
∴ So the GCF of the given numbers is 2 x 3 x 3 x 5 = 90
Greatest Common Factor of 5670,6840 By Matching Biggest Common Factor Method
Now, list down the factors of 5670
:1,2,3,5,6,7,9,10,14,15,18,21,27,30,35,42,45,54,63,70,81,90,105,126,135,162,189,210,270,315,378,405,567,630,810,945,1134,1890,2835,5670
Now, list down the factors of 6840
:1,2,3,4,5,6,8,9,10,12,15,18,19,20,24,30,36,38,40,45,57,60,72,76,90,95,114,120,152,171,180,190,228,285,342,360,380,456,570,684,760,855,1140,1368,1710,2280,3420,6840
Greatest Common Factor
We found the factors 5670,6840 . The biggest common factor number is the GCF number.
So the greatest common factor 5670,6840 is 90.
Lets's calculate LCM of 281,331
Given numbers has no common factors except 1. So, there LCM is their product i.e 93011
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 90/93011
Therefore, the GCF of Fractions 5670/281,6840/331 is 90/93011
Least Common Multiple of 281,331 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 281,331 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(281,331) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(281,331) x common factors =1 x 1 = 1
LCM(281,331) = ( 281 × 331 ) / 1
LCM(281,331) = 93011 / 1
LCM(281,331) = 93011
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FAQs on GCF of Fractions of 5670/281, 6840/331
1. What is the HCF of 5670,6840?
The HCF of 5670,6840 is 90
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 5670/281, 6840/331?
Answer: GCF of Numerators as per given numbers 5670/281, 6840/331 is
GCF of Numerators i.e. for 5670,6840 is 90
LCM of denominators i.e. for 281,331 is 93011.
Thus, GCF of Fractions is 90/93011.Finally, GCF of Fractions for 5670/281, 6840/331 is 90/93011.