GCF of 2040/426, 7820/7417
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 2040/426, 7820/7417 i.e 340/3159642 easily. The following is the detailed procedure to determine the greatest common factor of fractions 2040/426, 7820/7417.
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 2040/426,7820/7417?
Given fractions are 2040/426,7820/7417
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 2040/426,7820/7417, numerators are 2040,7820
Denominators are 426,7417
The GCF of 2040,7820 is 340 .
LCM of 426,7417 is 3159642.
The greatest common factor of 2040/426,7820/7417 = [GCF of 2040,7820]/[LCM of 426,7417]= 340/3159642
Therefore, the GCF of 2040/426,7820/7417 is 340/3159642.
To find the highest common factor of 2040,7820, we have to find the factors of both numbers and list the highest common factor.
The factors of 2040 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 17, 20, 24, 30, 34, 40, 51, 60, 68, 85, 102, 120, 136, 170, 204, 255, 340, 408, 510, 680, 1020, 2040
The factors of 7820 are 1, 2, 4, 5, 10, 17, 20, 23, 34, 46, 68, 85, 92, 115, 170, 230, 340, 391, 460, 782, 1564, 1955, 3910, 7820
The HCF of 2040,7820 is 340.
Lets's calculate GCF of 2040,7820
| 2 | 2040, 7820 |
| 2 | 1020, 3910 |
| 5 | 510, 1955 |
| 17 | 102, 391 |
| 6, 23 |
∴ So the GCF of the given numbers is 2 x 2 x 5 x 17 = 340
Greatest Common Factor of 2040,7820 By Matching Biggest Common Factor Method
Now, list down the factors of 2040
:1,2,3,4,5,6,8,10,12,15,17,20,24,30,34,40,51,60,68,85,102,120,136,170,204,255,340,408,510,680,1020,2040
Now, list down the factors of 7820
:1,2,4,5,10,17,20,23,34,46,68,85,92,115,170,230,340,391,460,782,1564,1955,3910,7820
Greatest Common Factor
We found the factors 2040,7820 . The biggest common factor number is the GCF number.
So the greatest common factor 2040,7820 is 340.
Lets's calculate LCM of 426,7417
Given numbers has no common factors except 1. So, there LCM is their product i.e 3159642
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 340/3159642
Therefore, the GCF of Fractions 2040/426,7820/7417 is 340/3159642
Least Common Multiple of 426,7417 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 426,7417 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(426,7417) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(426,7417) x common factors =1 x 1 = 1
LCM(426,7417) = ( 426 × 7417 ) / 1
LCM(426,7417) = 3159642 / 1
LCM(426,7417) = 3159642
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FAQs on GCF of Fractions of 2040/426, 7820/7417
1. What is the HCF of 2040,7820?
The HCF of 2040,7820 is 340
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 2040/426, 7820/7417?
Answer: GCF of Numerators as per given numbers 2040/426, 7820/7417 is
GCF of Numerators i.e. for 2040,7820 is 340
LCM of denominators i.e. for 426,7417 is 3159642.
Thus, GCF of Fractions is 340/3159642.Finally, GCF of Fractions for 2040/426, 7820/7417 is 340/3159642.