GCF of 1500/760, 1720/3494
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1500/760, 1720/3494 i.e 20/1327720 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1500/760, 1720/3494.
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 1500/760,1720/3494?
Given fractions are 1500/760,1720/3494
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 1500/760,1720/3494, numerators are 1500,1720
Denominators are 760,3494
The GCF of 1500,1720 is 20 .
LCM of 760,3494 is 1327720.
The greatest common factor of 1500/760,1720/3494 = [GCF of 1500,1720]/[LCM of 760,3494]= 20/1327720
Therefore, the GCF of 1500/760,1720/3494 is 20/1327720.
To find the highest common factor of 1500,1720, we have to find the factors of both numbers and list the highest common factor.
The factors of 1500 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 125, 150, 250, 300, 375, 500, 750, 1500
The factors of 1720 are 1, 2, 4, 5, 8, 10, 20, 40, 43, 86, 172, 215, 344, 430, 860, 1720
The HCF of 1500,1720 is 20.
Lets's calculate GCF of 1500,1720
| 2 | 1500, 1720 |
| 2 | 750, 860 |
| 5 | 375, 430 |
| 75, 86 |
∴ So the GCF of the given numbers is 2 x 2 x 5 = 20
Greatest Common Factor of 1500,1720 By Matching Biggest Common Factor Method
Now, list down the factors of 1500
:1,2,3,4,5,6,10,12,15,20,25,30,50,60,75,100,125,150,250,300,375,500,750,1500
Now, list down the factors of 1720
:1,2,4,5,8,10,20,40,43,86,172,215,344,430,860,1720
Greatest Common Factor
We found the factors 1500,1720 . The biggest common factor number is the GCF number.
So the greatest common factor 1500,1720 is 20.
Lets's calculate LCM of 760,3494
| 2 | 760, 3494 |
| 380, 1747 |
∴ So the LCM of the given numbers is 2 x 380 x 1747 = 1327720
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 20/1327720
Therefore, the GCF of Fractions 1500/760,1720/3494 is 20/1327720
Least Common Multiple of 760,3494 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 760,3494 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(760,3494) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(760,3494) x common factors =2 x 1 = 2
LCM(760,3494) = ( 760 × 3494 ) / 2
LCM(760,3494) = 2655440 / 2
LCM(760,3494) = 1327720
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FAQs on GCF of Fractions of 1500/760, 1720/3494
1. What is the HCF of 1500,1720?
The HCF of 1500,1720 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 1500/760, 1720/3494?
Answer: GCF of Numerators as per given numbers 1500/760, 1720/3494 is
GCF of Numerators i.e. for 1500,1720 is 20
LCM of denominators i.e. for 760,3494 is 1327720.
Thus, GCF of Fractions is 20/1327720.Finally, GCF of Fractions for 1500/760, 1720/3494 is 20/1327720.