GCF of 7192/414, 9156/669
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 7192/414, 9156/669 i.e 4/92322 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7192/414, 9156/669.
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 7192/414,9156/669?
Given fractions are 7192/414,9156/669
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 7192/414,9156/669, numerators are 7192,9156
Denominators are 414,669
The GCF of 7192,9156 is 4 .
LCM of 414,669 is 92322.
The greatest common factor of 7192/414,9156/669 = [GCF of 7192,9156]/[LCM of 414,669]= 4/92322
Therefore, the GCF of 7192/414,9156/669 is 4/92322.
To find the highest common factor of 7192,9156, we have to find the factors of both numbers and list the highest common factor.
The factors of 7192 are 1, 2, 4, 8, 29, 31, 58, 62, 116, 124, 232, 248, 899, 1798, 3596, 7192
The factors of 9156 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84, 109, 218, 327, 436, 654, 763, 1308, 1526, 2289, 3052, 4578, 9156
The HCF of 7192,9156 is 4.
Lets's calculate GCF of 7192,9156
| 2 | 7192, 9156 |
| 2 | 3596, 4578 |
| 1798, 2289 |
∴ So the GCF of the given numbers is 2 x 2 = 4
Greatest Common Factor of 7192,9156 By Matching Biggest Common Factor Method
Now, list down the factors of 7192
:1,2,4,8,29,31,58,62,116,124,232,248,899,1798,3596,7192
Now, list down the factors of 9156
:1,2,3,4,6,7,12,14,21,28,42,84,109,218,327,436,654,763,1308,1526,2289,3052,4578,9156
Greatest Common Factor
We found the factors 7192,9156 . The biggest common factor number is the GCF number.
So the greatest common factor 7192,9156 is 4.
Lets's calculate LCM of 414,669
| 3 | 414, 669 |
| 138, 223 |
∴ So the LCM of the given numbers is 3 x 138 x 223 = 92322
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/92322
Therefore, the GCF of Fractions 7192/414,9156/669 is 4/92322
Least Common Multiple of 414,669 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 414,669 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(414,669) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(414,669) x common factors =3 x 1 = 3
LCM(414,669) = ( 414 × 669 ) / 3
LCM(414,669) = 276966 / 3
LCM(414,669) = 92322
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FAQs on GCF of Fractions of 7192/414, 9156/669
1. What is the HCF of 7192,9156?
The HCF of 7192,9156 is 4
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 7192/414, 9156/669?
Answer: GCF of Numerators as per given numbers 7192/414, 9156/669 is
GCF of Numerators i.e. for 7192,9156 is 4
LCM of denominators i.e. for 414,669 is 92322.
Thus, GCF of Fractions is 4/92322.Finally, GCF of Fractions for 7192/414, 9156/669 is 4/92322.