GCF of 6706/770, 6174/1271
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 6706/770, 6174/1271 i.e 14/978670 easily. The following is the detailed procedure to determine the greatest common factor of fractions 6706/770, 6174/1271.
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 6706/770,6174/1271?
Given fractions are 6706/770,6174/1271
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 6706/770,6174/1271, numerators are 6706,6174
Denominators are 770,1271
The GCF of 6706,6174 is 14 .
LCM of 770,1271 is 978670.
The greatest common factor of 6706/770,6174/1271 = [GCF of 6706,6174]/[LCM of 770,1271]= 14/978670
Therefore, the GCF of 6706/770,6174/1271 is 14/978670.
To find the highest common factor of 6706,6174, we have to find the factors of both numbers and list the highest common factor.
The factors of 6706 are 1, 2, 7, 14, 479, 958, 3353, 6706
The factors of 6174 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 49, 63, 98, 126, 147, 294, 343, 441, 686, 882, 1029, 2058, 3087, 6174
The HCF of 6706,6174 is 14.
Lets's calculate GCF of 6706,6174
| 2 | 6706, 6174 |
| 7 | 3353, 3087 |
| 479, 441 |
∴ So the GCF of the given numbers is 2 x 7 = 14
Greatest Common Factor of 6706,6174 By Matching Biggest Common Factor Method
Now, list down the factors of 6706
:1,2,7,14,479,958,3353,6706
Now, list down the factors of 6174
:1,2,3,6,7,9,14,18,21,42,49,63,98,126,147,294,343,441,686,882,1029,2058,3087,6174
Greatest Common Factor
We found the factors 6706,6174 . The biggest common factor number is the GCF number.
So the greatest common factor 6706,6174 is 14.
Lets's calculate LCM of 770,1271
Given numbers has no common factors except 1. So, there LCM is their product i.e 978670
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 14/978670
Therefore, the GCF of Fractions 6706/770,6174/1271 is 14/978670
Least Common Multiple of 770,1271 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 770,1271 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(770,1271) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(770,1271) x common factors =1 x 1 = 1
LCM(770,1271) = ( 770 × 1271 ) / 1
LCM(770,1271) = 978670 / 1
LCM(770,1271) = 978670
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FAQs on GCF of Fractions of 6706/770, 6174/1271
1. What is the HCF of 6706,6174?
The HCF of 6706,6174 is 14
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 6706/770, 6174/1271?
Answer: GCF of Numerators as per given numbers 6706/770, 6174/1271 is
GCF of Numerators i.e. for 6706,6174 is 14
LCM of denominators i.e. for 770,1271 is 978670.
Thus, GCF of Fractions is 14/978670.Finally, GCF of Fractions for 6706/770, 6174/1271 is 14/978670.