GCF of 712/67, 798/686
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 712/67, 798/686 i.e 2/45962 easily. The following is the detailed procedure to determine the greatest common factor of fractions 712/67, 798/686.
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 712/67,798/686?
Given fractions are 712/67,798/686
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 712/67,798/686, numerators are 712,798
Denominators are 67,686
The GCF of 712,798 is 2 .
LCM of 67,686 is 45962.
The greatest common factor of 712/67,798/686 = [GCF of 712,798]/[LCM of 67,686]= 2/45962
Therefore, the GCF of 712/67,798/686 is 2/45962.
To find the highest common factor of 712,798, 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 798 are 1, 2, 3, 6, 7, 14, 19, 21, 38, 42, 57, 114, 133, 266, 399, 798
The HCF of 712,798 is 2.
Lets's calculate GCF of 712,798
| 2 | 712, 798 |
| 356, 399 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 712,798 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 798
:1,2,3,6,7,14,19,21,38,42,57,114,133,266,399,798
Greatest Common Factor
We found the factors 712,798 . The biggest common factor number is the GCF number.
So the greatest common factor 712,798 is 2.
Lets's calculate LCM of 67,686
Given numbers has no common factors except 1. So, there LCM is their product i.e 45962
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/45962
Therefore, the GCF of Fractions 712/67,798/686 is 2/45962
Least Common Multiple of 67,686 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 67,686 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(67,686) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(67,686) x common factors =1 x 1 = 1
LCM(67,686) = ( 67 × 686 ) / 1
LCM(67,686) = 45962 / 1
LCM(67,686) = 45962
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FAQs on GCF of Fractions of 712/67, 798/686
1. What is the HCF of 712,798?
The HCF of 712,798 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 712/67, 798/686?
Answer: GCF of Numerators as per given numbers 712/67, 798/686 is
GCF of Numerators i.e. for 712,798 is 2
LCM of denominators i.e. for 67,686 is 45962.
Thus, GCF of Fractions is 2/45962.Finally, GCF of Fractions for 712/67, 798/686 is 2/45962.