GCF of 705/122, 660/579
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 705/122, 660/579 i.e 15/70638 easily. The following is the detailed procedure to determine the greatest common factor of fractions 705/122, 660/579.
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 705/122,660/579?
Given fractions are 705/122,660/579
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 705/122,660/579, numerators are 705,660
Denominators are 122,579
The GCF of 705,660 is 15 .
LCM of 122,579 is 70638.
The greatest common factor of 705/122,660/579 = [GCF of 705,660]/[LCM of 122,579]= 15/70638
Therefore, the GCF of 705/122,660/579 is 15/70638.
To find the highest common factor of 705,660, we have to find the factors of both numbers and list the highest common factor.
The factors of 705 are 1, 3, 5, 15, 47, 141, 235, 705
The factors of 660 are 1, 2, 3, 4, 5, 6, 10, 11, 12, 15, 20, 22, 30, 33, 44, 55, 60, 66, 110, 132, 165, 220, 330, 660
The HCF of 705,660 is 15.
Lets's calculate GCF of 705,660
| 3 | 705, 660 |
| 5 | 235, 220 |
| 47, 44 |
∴ So the GCF of the given numbers is 3 x 5 = 15
Greatest Common Factor of 705,660 By Matching Biggest Common Factor Method
Now, list down the factors of 705
:1,3,5,15,47,141,235,705
Now, list down the factors of 660
:1,2,3,4,5,6,10,11,12,15,20,22,30,33,44,55,60,66,110,132,165,220,330,660
Greatest Common Factor
We found the factors 705,660 . The biggest common factor number is the GCF number.
So the greatest common factor 705,660 is 15.
Lets's calculate LCM of 122,579
Given numbers has no common factors except 1. So, there LCM is their product i.e 70638
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 15/70638
Therefore, the GCF of Fractions 705/122,660/579 is 15/70638
Least Common Multiple of 122,579 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 122,579 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(122,579) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(122,579) x common factors =1 x 1 = 1
LCM(122,579) = ( 122 × 579 ) / 1
LCM(122,579) = 70638 / 1
LCM(122,579) = 70638
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FAQs on GCF of Fractions of 705/122, 660/579
1. What is the HCF of 705,660?
The HCF of 705,660 is 15
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 705/122, 660/579?
Answer: GCF of Numerators as per given numbers 705/122, 660/579 is
GCF of Numerators i.e. for 705,660 is 15
LCM of denominators i.e. for 122,579 is 70638.
Thus, GCF of Fractions is 15/70638.Finally, GCF of Fractions for 705/122, 660/579 is 15/70638.