GCF of 712/595, 1869/219
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 712/595, 1869/219 i.e 89/130305 easily. The following is the detailed procedure to determine the greatest common factor of fractions 712/595, 1869/219.
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 712/595,1869/219?
Given fractions are 712/595,1869/219
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 712/595,1869/219, numerators are 712,1869
Denominators are 595,219
The GCF of 712,1869 is 89 .
LCM of 595,219 is 130305.
The greatest common factor of 712/595,1869/219 = [GCF of 712,1869]/[LCM of 595,219]= 89/130305
Therefore, the GCF of 712/595,1869/219 is 89/130305.
To find the highest common factor of 712,1869, we have to find the factors of both numbers and list the highest common factor.
The factors of 712 are 1, 2, 4, 8, 89, 178, 356, 712
The factors of 1869 are 1, 3, 7, 21, 89, 267, 623, 1869
The HCF of 712,1869 is 89.
Lets's calculate GCF of 712,1869
| 89 | 712, 1869 |
| 8, 21 |
∴ So the GCF of the given numbers is 89 = 89
Greatest Common Factor of 712,1869 By Matching Biggest Common Factor Method
Now, list down the factors of 712
:1,2,4,8,89,178,356,712
Now, list down the factors of 1869
:1,3,7,21,89,267,623,1869
Greatest Common Factor
We found the factors 712,1869 . The biggest common factor number is the GCF number.
So the greatest common factor 712,1869 is 89.
Lets's calculate LCM of 595,219
Given numbers has no common factors except 1. So, there LCM is their product i.e 130305
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 89/130305
Therefore, the GCF of Fractions 712/595,1869/219 is 89/130305
Least Common Multiple of 595,219 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 595,219 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(595,219) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(595,219) x common factors =1 x 1 = 1
LCM(595,219) = ( 595 × 219 ) / 1
LCM(595,219) = 130305 / 1
LCM(595,219) = 130305
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FAQs on GCF of Fractions of 712/595, 1869/219
1. What is the HCF of 712,1869?
The HCF of 712,1869 is 89
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 712/595, 1869/219?
Answer: GCF of Numerators as per given numbers 712/595, 1869/219 is
GCF of Numerators i.e. for 712,1869 is 89
LCM of denominators i.e. for 595,219 is 130305.
Thus, GCF of Fractions is 89/130305.Finally, GCF of Fractions for 712/595, 1869/219 is 89/130305.