GCF of 3020/765, 1982/5742
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 3020/765, 1982/5742 i.e 2/488070 easily. The following is the detailed procedure to determine the greatest common factor of fractions 3020/765, 1982/5742.
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 3020/765,1982/5742?
Given fractions are 3020/765,1982/5742
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 3020/765,1982/5742, numerators are 3020,1982
Denominators are 765,5742
The GCF of 3020,1982 is 2 .
LCM of 765,5742 is 488070.
The greatest common factor of 3020/765,1982/5742 = [GCF of 3020,1982]/[LCM of 765,5742]= 2/488070
Therefore, the GCF of 3020/765,1982/5742 is 2/488070.
To find the highest common factor of 3020,1982, we have to find the factors of both numbers and list the highest common factor.
The factors of 3020 are 1, 2, 4, 5, 10, 20, 151, 302, 604, 755, 1510, 3020
The factors of 1982 are 1, 2, 991, 1982
The HCF of 3020,1982 is 2.
Lets's calculate GCF of 3020,1982
| 2 | 3020, 1982 |
| 1510, 991 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 3020,1982 By Matching Biggest Common Factor Method
Now, list down the factors of 3020
:1,2,4,5,10,20,151,302,604,755,1510,3020
Now, list down the factors of 1982
:1,2,991,1982
Greatest Common Factor
We found the factors 3020,1982 . The biggest common factor number is the GCF number.
So the greatest common factor 3020,1982 is 2.
Lets's calculate LCM of 765,5742
| 3 | 765, 5742 |
| 3 | 255, 1914 |
| 85, 638 |
∴ So the LCM of the given numbers is 3 x 3 x 85 x 638 = 488070
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/488070
Therefore, the GCF of Fractions 3020/765,1982/5742 is 2/488070
Least Common Multiple of 765,5742 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 765,5742 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(765,5742) = 9
common factors(in case of two or more numbers have common factors) = 1
GCF(765,5742) x common factors =9 x 1 = 9
LCM(765,5742) = ( 765 × 5742 ) / 9
LCM(765,5742) = 4392630 / 9
LCM(765,5742) = 488070
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FAQs on GCF of Fractions of 3020/765, 1982/5742
1. What is the HCF of 3020,1982?
The HCF of 3020,1982 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 3020/765, 1982/5742?
Answer: GCF of Numerators as per given numbers 3020/765, 1982/5742 is
GCF of Numerators i.e. for 3020,1982 is 2
LCM of denominators i.e. for 765,5742 is 488070.
Thus, GCF of Fractions is 2/488070.Finally, GCF of Fractions for 3020/765, 1982/5742 is 2/488070.