GCF of 1720/714, 2782/4056
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1720/714, 2782/4056 i.e 2/482664 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1720/714, 2782/4056.
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 1720/714,2782/4056?
Given fractions are 1720/714,2782/4056
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 1720/714,2782/4056, numerators are 1720,2782
Denominators are 714,4056
The GCF of 1720,2782 is 2 .
LCM of 714,4056 is 482664.
The greatest common factor of 1720/714,2782/4056 = [GCF of 1720,2782]/[LCM of 714,4056]= 2/482664
Therefore, the GCF of 1720/714,2782/4056 is 2/482664.
To find the highest common factor of 1720,2782, we have to find the factors of both numbers and list the highest common factor.
The factors of 1720 are 1, 2, 4, 5, 8, 10, 20, 40, 43, 86, 172, 215, 344, 430, 860, 1720
The factors of 2782 are 1, 2, 13, 26, 107, 214, 1391, 2782
The HCF of 1720,2782 is 2.
Lets's calculate GCF of 1720,2782
| 2 | 1720, 2782 |
| 860, 1391 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 1720,2782 By Matching Biggest Common Factor Method
Now, list down the factors of 1720
:1,2,4,5,8,10,20,40,43,86,172,215,344,430,860,1720
Now, list down the factors of 2782
:1,2,13,26,107,214,1391,2782
Greatest Common Factor
We found the factors 1720,2782 . The biggest common factor number is the GCF number.
So the greatest common factor 1720,2782 is 2.
Lets's calculate LCM of 714,4056
| 2 | 714, 4056 |
| 3 | 357, 2028 |
| 119, 676 |
∴ So the LCM of the given numbers is 2 x 3 x 119 x 676 = 482664
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/482664
Therefore, the GCF of Fractions 1720/714,2782/4056 is 2/482664
Least Common Multiple of 714,4056 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 714,4056 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(714,4056) = 6
common factors(in case of two or more numbers have common factors) = 1
GCF(714,4056) x common factors =6 x 1 = 6
LCM(714,4056) = ( 714 × 4056 ) / 6
LCM(714,4056) = 2895984 / 6
LCM(714,4056) = 482664
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FAQs on GCF of Fractions of 1720/714, 2782/4056
1. What is the HCF of 1720,2782?
The HCF of 1720,2782 is 2
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 1720/714, 2782/4056?
Answer: GCF of Numerators as per given numbers 1720/714, 2782/4056 is
GCF of Numerators i.e. for 1720,2782 is 2
LCM of denominators i.e. for 714,4056 is 482664.
Thus, GCF of Fractions is 2/482664.Finally, GCF of Fractions for 1720/714, 2782/4056 is 2/482664.