GCF of 7077/414, 2232/6832
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 7077/414, 2232/6832 i.e 3/1414224 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7077/414, 2232/6832.
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 7077/414,2232/6832?
Given fractions are 7077/414,2232/6832
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 7077/414,2232/6832, numerators are 7077,2232
Denominators are 414,6832
The GCF of 7077,2232 is 3 .
LCM of 414,6832 is 1414224.
The greatest common factor of 7077/414,2232/6832 = [GCF of 7077,2232]/[LCM of 414,6832]= 3/1414224
Therefore, the GCF of 7077/414,2232/6832 is 3/1414224.
To find the highest common factor of 7077,2232, we have to find the factors of both numbers and list the highest common factor.
The factors of 7077 are 1, 3, 7, 21, 337, 1011, 2359, 7077
The factors of 2232 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 31, 36, 62, 72, 93, 124, 186, 248, 279, 372, 558, 744, 1116, 2232
The HCF of 7077,2232 is 3.
Lets's calculate GCF of 7077,2232
| 3 | 7077, 2232 |
| 2359, 744 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 7077,2232 By Matching Biggest Common Factor Method
Now, list down the factors of 7077
:1,3,7,21,337,1011,2359,7077
Now, list down the factors of 2232
:1,2,3,4,6,8,9,12,18,24,31,36,62,72,93,124,186,248,279,372,558,744,1116,2232
Greatest Common Factor
We found the factors 7077,2232 . The biggest common factor number is the GCF number.
So the greatest common factor 7077,2232 is 3.
Lets's calculate LCM of 414,6832
| 2 | 414, 6832 |
| 207, 3416 |
∴ So the LCM of the given numbers is 2 x 207 x 3416 = 1414224
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/1414224
Therefore, the GCF of Fractions 7077/414,2232/6832 is 3/1414224
Least Common Multiple of 414,6832 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 414,6832 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(414,6832) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(414,6832) x common factors =2 x 1 = 2
LCM(414,6832) = ( 414 × 6832 ) / 2
LCM(414,6832) = 2828448 / 2
LCM(414,6832) = 1414224
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FAQs on GCF of Fractions of 7077/414, 2232/6832
1. What is the HCF of 7077,2232?
The HCF of 7077,2232 is 3
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 7077/414, 2232/6832?
Answer: GCF of Numerators as per given numbers 7077/414, 2232/6832 is
GCF of Numerators i.e. for 7077,2232 is 3
LCM of denominators i.e. for 414,6832 is 1414224.
Thus, GCF of Fractions is 3/1414224.Finally, GCF of Fractions for 7077/414, 2232/6832 is 3/1414224.