GCF of 10/65, 817/42, 590/360
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 10/65, 817/42, 590/360 i.e 1/32760 easily. The following is the detailed procedure to determine the greatest common factor of fractions 10/65, 817/42, 590/360.
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 10/65,817/42,590/360?
Given fractions are 10/65,817/42,590/360
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 10/65,817/42,590/360, numerators are 10,817,590
Denominators are 65,42,360
The GCF of 10,817,590 is 1 .
LCM of 65,42,360 is 32760.
The greatest common factor of 10/65,817/42,590/360 = [GCF of 10,817,590]/[LCM of 65,42,360]= 1/32760
Therefore, the GCF of 10/65,817/42,590/360 is 1/32760.
To find the highest common factor of 10,817,590, we have to find the factors of both numbers and list the highest common factor.
The factors of 10 are 1, 2, 5, 10
The factors of 817 are 1, 19, 43, 817
The factors of 590 are 1, 2, 5, 10, 59, 118, 295, 590
The HCF of 10,817,590 is 1.
Lets's calculate GCF of 10,817,590
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 10,817,590 By Matching Biggest Common Factor Method
Now, list down the factors of 10
:1,2,5,10
Now, list down the factors of 817
:1,19,43,817
Now, list down the factors of 590
:1,2,5,10,59,118,295,590
Greatest Common Factor
We found the factors 10,817,590 . The biggest common factor number is the GCF number.
So the greatest common factor 10,817,590 is 1.
Lets's calculate LCM of 65,42,360
| 2 | 65, 42, 360 |
| 3 | 65, 21, 180 |
| 5 | 65, 7, 60 |
| 13, 7, 12 |
∴ So the LCM of the given numbers is 2 x 3 x 5 x 13 x 7 x 12 = 32760
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/32760
Therefore, the GCF of Fractions 10/65,817/42,590/360 is 1/32760
Least Common Multiple of 65,42,360 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 65,42,360 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(65,42,360) = 1
common factors(in case of two or more numbers have common factors) = 30
GCF(65,42,360) x common factors =1 x 30 = 30
LCM(65,42,360) = ( 65 × 42 × 360 ) / 30
LCM(65,42,360) = 982800 / 30
LCM(65,42,360) = 32760
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FAQs on GCF of Fractions of 10/65, 817/42, 590/360
1. What is the HCF of 10,817,590?
The HCF of 10,817,590 is 1
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 10/65, 817/42, 590/360?
Answer: GCF of Numerators as per given numbers 10/65, 817/42, 590/360 is
GCF of Numerators i.e. for 10,817,590 is 1
LCM of denominators i.e. for 65,42,360 is 32760.
Thus, GCF of Fractions is 1/32760.Finally, GCF of Fractions for 10/65, 817/42, 590/360 is 1/32760.