GCF of 6019/312, 7122/9750
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 6019/312, 7122/9750 i.e 1/39000 easily. The following is the detailed procedure to determine the greatest common factor of fractions 6019/312, 7122/9750.
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 6019/312,7122/9750?
Given fractions are 6019/312,7122/9750
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 6019/312,7122/9750, numerators are 6019,7122
Denominators are 312,9750
The GCF of 6019,7122 is 1 .
LCM of 312,9750 is 39000.
The greatest common factor of 6019/312,7122/9750 = [GCF of 6019,7122]/[LCM of 312,9750]= 1/39000
Therefore, the GCF of 6019/312,7122/9750 is 1/39000.
To find the highest common factor of 6019,7122, we have to find the factors of both numbers and list the highest common factor.
The factors of 6019 are 1, 13, 463, 6019
The factors of 7122 are 1, 2, 3, 6, 1187, 2374, 3561, 7122
The HCF of 6019,7122 is 1.
Lets's calculate GCF of 6019,7122
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 6019,7122 By Matching Biggest Common Factor Method
Now, list down the factors of 6019
:1,13,463,6019
Now, list down the factors of 7122
:1,2,3,6,1187,2374,3561,7122
Greatest Common Factor
We found the factors 6019,7122 . The biggest common factor number is the GCF number.
So the greatest common factor 6019,7122 is 1.
Lets's calculate LCM of 312,9750
| 2 | 312, 9750 |
| 3 | 156, 4875 |
| 13 | 52, 1625 |
| 4, 125 |
∴ So the LCM of the given numbers is 2 x 3 x 13 x 4 x 125 = 39000
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/39000
Therefore, the GCF of Fractions 6019/312,7122/9750 is 1/39000
Least Common Multiple of 312,9750 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 312,9750 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(312,9750) = 78
common factors(in case of two or more numbers have common factors) = 1
GCF(312,9750) x common factors =78 x 1 = 78
LCM(312,9750) = ( 312 × 9750 ) / 78
LCM(312,9750) = 3042000 / 78
LCM(312,9750) = 39000
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FAQs on GCF of Fractions of 6019/312, 7122/9750
1. What is the HCF of 6019,7122?
The HCF of 6019,7122 is 1
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 6019/312, 7122/9750?
Answer: GCF of Numerators as per given numbers 6019/312, 7122/9750 is
GCF of Numerators i.e. for 6019,7122 is 1
LCM of denominators i.e. for 312,9750 is 39000.
Thus, GCF of Fractions is 1/39000.Finally, GCF of Fractions for 6019/312, 7122/9750 is 1/39000.