GCF of 20/701, 60/122, 300/169
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 20/701, 60/122, 300/169 i.e 20/14453218 easily. The following is the detailed procedure to determine the greatest common factor of fractions 20/701, 60/122, 300/169.
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 20/701,60/122,300/169?
Given fractions are 20/701,60/122,300/169
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 20/701,60/122,300/169, numerators are 20,60,300
Denominators are 701,122,169
The GCF of 20,60,300 is 20 .
LCM of 701,122,169 is 14453218.
The greatest common factor of 20/701,60/122,300/169 = [GCF of 20,60,300]/[LCM of 701,122,169]= 20/14453218
Therefore, the GCF of 20/701,60/122,300/169 is 20/14453218.
To find the highest common factor of 20,60,300, we have to find the factors of both numbers and list the highest common factor.
The factors of 20 are 1, 2, 4, 5, 10, 20
The factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
The factors of 300 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, 300
The HCF of 20,60,300 is 20.
Lets's calculate GCF of 20,60,300
| 2 | 20, 60, 300 |
| 2 | 10, 30, 150 |
| 5 | 5, 15, 75 |
| 1, 3, 15 |
∴ So the GCF of the given numbers is 2 x 2 x 5 = 20
Greatest Common Factor of 20,60,300 By Matching Biggest Common Factor Method
Now, list down the factors of 20
:1,2,4,5,10,20
Now, list down the factors of 60
:1,2,3,4,5,6,10,12,15,20,30,60
Now, list down the factors of 300
:1,2,3,4,5,6,10,12,15,20,25,30,50,60,75,100,150,300
Greatest Common Factor
We found the factors 20,60,300 . The biggest common factor number is the GCF number.
So the greatest common factor 20,60,300 is 20.
Lets's calculate LCM of 701,122,169
Given numbers has no common factors except 1. So, there LCM is their product i.e 14453218
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 20/14453218
Therefore, the GCF of Fractions 20/701,60/122,300/169 is 20/14453218
Least Common Multiple of 701,122,169 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 701,122,169 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(701,122,169) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(701,122,169) x common factors =1 x 1 = 1
LCM(701,122,169) = ( 701 × 122 × 169 ) / 1
LCM(701,122,169) = 14453218 / 1
LCM(701,122,169) = 14453218
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FAQs on GCF of Fractions of 20/701, 60/122, 300/169
1. What is the HCF of 20,60,300?
The HCF of 20,60,300 is 20
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 20/701, 60/122, 300/169?
Answer: GCF of Numerators as per given numbers 20/701, 60/122, 300/169 is
GCF of Numerators i.e. for 20,60,300 is 20
LCM of denominators i.e. for 701,122,169 is 14453218.
Thus, GCF of Fractions is 20/14453218.Finally, GCF of Fractions for 20/701, 60/122, 300/169 is 20/14453218.