GCF of 1970/782, 7080/9785
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1970/782, 7080/9785 i.e 10/7651870 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1970/782, 7080/9785.
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 1970/782,7080/9785?
Given fractions are 1970/782,7080/9785
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 1970/782,7080/9785, numerators are 1970,7080
Denominators are 782,9785
The GCF of 1970,7080 is 10 .
LCM of 782,9785 is 7651870.
The greatest common factor of 1970/782,7080/9785 = [GCF of 1970,7080]/[LCM of 782,9785]= 10/7651870
Therefore, the GCF of 1970/782,7080/9785 is 10/7651870.
To find the highest common factor of 1970,7080, we have to find the factors of both numbers and list the highest common factor.
The factors of 1970 are 1, 2, 5, 10, 197, 394, 985, 1970
The factors of 7080 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 59, 60, 118, 120, 177, 236, 295, 354, 472, 590, 708, 885, 1180, 1416, 1770, 2360, 3540, 7080
The HCF of 1970,7080 is 10.
Lets's calculate GCF of 1970,7080
| 2 | 1970, 7080 |
| 5 | 985, 3540 |
| 197, 708 |
∴ So the GCF of the given numbers is 2 x 5 = 10
Greatest Common Factor of 1970,7080 By Matching Biggest Common Factor Method
Now, list down the factors of 1970
:1,2,5,10,197,394,985,1970
Now, list down the factors of 7080
:1,2,3,4,5,6,8,10,12,15,20,24,30,40,59,60,118,120,177,236,295,354,472,590,708,885,1180,1416,1770,2360,3540,7080
Greatest Common Factor
We found the factors 1970,7080 . The biggest common factor number is the GCF number.
So the greatest common factor 1970,7080 is 10.
Lets's calculate LCM of 782,9785
Given numbers has no common factors except 1. So, there LCM is their product i.e 7651870
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 10/7651870
Therefore, the GCF of Fractions 1970/782,7080/9785 is 10/7651870
Least Common Multiple of 782,9785 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 782,9785 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(782,9785) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(782,9785) x common factors =1 x 1 = 1
LCM(782,9785) = ( 782 × 9785 ) / 1
LCM(782,9785) = 7651870 / 1
LCM(782,9785) = 7651870
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FAQs on GCF of Fractions of 1970/782, 7080/9785
1. What is the HCF of 1970,7080?
The HCF of 1970,7080 is 10
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 1970/782, 7080/9785?
Answer: GCF of Numerators as per given numbers 1970/782, 7080/9785 is
GCF of Numerators i.e. for 1970,7080 is 10
LCM of denominators i.e. for 782,9785 is 7651870.
Thus, GCF of Fractions is 10/7651870.Finally, GCF of Fractions for 1970/782, 7080/9785 is 10/7651870.