GCF of 7769/414, 8074/7206
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 7769/414, 8074/7206 i.e 1/497214 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7769/414, 8074/7206.
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 7769/414,8074/7206?
Given fractions are 7769/414,8074/7206
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 7769/414,8074/7206, numerators are 7769,8074
Denominators are 414,7206
The GCF of 7769,8074 is 1 .
LCM of 414,7206 is 497214.
The greatest common factor of 7769/414,8074/7206 = [GCF of 7769,8074]/[LCM of 414,7206]= 1/497214
Therefore, the GCF of 7769/414,8074/7206 is 1/497214.
To find the highest common factor of 7769,8074, we have to find the factors of both numbers and list the highest common factor.
The factors of 7769 are 1, 17, 457, 7769
The factors of 8074 are 1, 2, 11, 22, 367, 734, 4037, 8074
The HCF of 7769,8074 is 1.
Lets's calculate GCF of 7769,8074
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 7769,8074 By Matching Biggest Common Factor Method
Now, list down the factors of 7769
:1,17,457,7769
Now, list down the factors of 8074
:1,2,11,22,367,734,4037,8074
Greatest Common Factor
We found the factors 7769,8074 . The biggest common factor number is the GCF number.
So the greatest common factor 7769,8074 is 1.
Lets's calculate LCM of 414,7206
| 2 | 414, 7206 |
| 3 | 207, 3603 |
| 69, 1201 |
∴ So the LCM of the given numbers is 2 x 3 x 69 x 1201 = 497214
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/497214
Therefore, the GCF of Fractions 7769/414,8074/7206 is 1/497214
Least Common Multiple of 414,7206 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 414,7206 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(414,7206) = 6
common factors(in case of two or more numbers have common factors) = 1
GCF(414,7206) x common factors =6 x 1 = 6
LCM(414,7206) = ( 414 × 7206 ) / 6
LCM(414,7206) = 2983284 / 6
LCM(414,7206) = 497214
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FAQs on GCF of Fractions of 7769/414, 8074/7206
1. What is the HCF of 7769,8074?
The HCF of 7769,8074 is 1
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 7769/414, 8074/7206?
Answer: GCF of Numerators as per given numbers 7769/414, 8074/7206 is
GCF of Numerators i.e. for 7769,8074 is 1
LCM of denominators i.e. for 414,7206 is 497214.
Thus, GCF of Fractions is 1/497214.Finally, GCF of Fractions for 7769/414, 8074/7206 is 1/497214.