GCF of 7677/27, 7182/694
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 7677/27, 7182/694 i.e 9/18738 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7677/27, 7182/694.
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 7677/27,7182/694?
Given fractions are 7677/27,7182/694
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 7677/27,7182/694, numerators are 7677,7182
Denominators are 27,694
The GCF of 7677,7182 is 9 .
LCM of 27,694 is 18738.
The greatest common factor of 7677/27,7182/694 = [GCF of 7677,7182]/[LCM of 27,694]= 9/18738
Therefore, the GCF of 7677/27,7182/694 is 9/18738.
To find the highest common factor of 7677,7182, we have to find the factors of both numbers and list the highest common factor.
The factors of 7677 are 1, 3, 9, 853, 2559, 7677
The factors of 7182 are 1, 2, 3, 6, 7, 9, 14, 18, 19, 21, 27, 38, 42, 54, 57, 63, 114, 126, 133, 171, 189, 266, 342, 378, 399, 513, 798, 1026, 1197, 2394, 3591, 7182
The HCF of 7677,7182 is 9.
Lets's calculate GCF of 7677,7182
| 3 | 7677, 7182 |
| 3 | 2559, 2394 |
| 853, 798 |
∴ So the GCF of the given numbers is 3 x 3 = 9
Greatest Common Factor of 7677,7182 By Matching Biggest Common Factor Method
Now, list down the factors of 7677
:1,3,9,853,2559,7677
Now, list down the factors of 7182
:1,2,3,6,7,9,14,18,19,21,27,38,42,54,57,63,114,126,133,171,189,266,342,378,399,513,798,1026,1197,2394,3591,7182
Greatest Common Factor
We found the factors 7677,7182 . The biggest common factor number is the GCF number.
So the greatest common factor 7677,7182 is 9.
Lets's calculate LCM of 27,694
Given numbers has no common factors except 1. So, there LCM is their product i.e 18738
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 9/18738
Therefore, the GCF of Fractions 7677/27,7182/694 is 9/18738
Least Common Multiple of 27,694 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 27,694 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(27,694) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(27,694) x common factors =1 x 1 = 1
LCM(27,694) = ( 27 × 694 ) / 1
LCM(27,694) = 18738 / 1
LCM(27,694) = 18738
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FAQs on GCF of Fractions of 7677/27, 7182/694
1. What is the HCF of 7677,7182?
The HCF of 7677,7182 is 9
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 7677/27, 7182/694?
Answer: GCF of Numerators as per given numbers 7677/27, 7182/694 is
GCF of Numerators i.e. for 7677,7182 is 9
LCM of denominators i.e. for 27,694 is 18738.
Thus, GCF of Fractions is 9/18738.Finally, GCF of Fractions for 7677/27, 7182/694 is 9/18738.