GCF of 544/414, 7174/786
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 544/414, 7174/786 i.e 34/54234 easily. The following is the detailed procedure to determine the greatest common factor of fractions 544/414, 7174/786.
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 544/414,7174/786?
Given fractions are 544/414,7174/786
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 544/414,7174/786, numerators are 544,7174
Denominators are 414,786
The GCF of 544,7174 is 34 .
LCM of 414,786 is 54234.
The greatest common factor of 544/414,7174/786 = [GCF of 544,7174]/[LCM of 414,786]= 34/54234
Therefore, the GCF of 544/414,7174/786 is 34/54234.
To find the highest common factor of 544,7174, we have to find the factors of both numbers and list the highest common factor.
The factors of 544 are 1, 2, 4, 8, 16, 17, 32, 34, 68, 136, 272, 544
The factors of 7174 are 1, 2, 17, 34, 211, 422, 3587, 7174
The HCF of 544,7174 is 34.
Lets's calculate GCF of 544,7174
| 2 | 544, 7174 |
| 17 | 272, 3587 |
| 16, 211 |
∴ So the GCF of the given numbers is 2 x 17 = 34
Greatest Common Factor of 544,7174 By Matching Biggest Common Factor Method
Now, list down the factors of 544
:1,2,4,8,16,17,32,34,68,136,272,544
Now, list down the factors of 7174
:1,2,17,34,211,422,3587,7174
Greatest Common Factor
We found the factors 544,7174 . The biggest common factor number is the GCF number.
So the greatest common factor 544,7174 is 34.
Lets's calculate LCM of 414,786
| 2 | 414, 786 |
| 3 | 207, 393 |
| 69, 131 |
∴ So the LCM of the given numbers is 2 x 3 x 69 x 131 = 54234
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 34/54234
Therefore, the GCF of Fractions 544/414,7174/786 is 34/54234
Least Common Multiple of 414,786 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 414,786 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(414,786) = 6
common factors(in case of two or more numbers have common factors) = 1
GCF(414,786) x common factors =6 x 1 = 6
LCM(414,786) = ( 414 × 786 ) / 6
LCM(414,786) = 325404 / 6
LCM(414,786) = 54234
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FAQs on GCF of Fractions of 544/414, 7174/786
1. What is the HCF of 544,7174?
The HCF of 544,7174 is 34
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 544/414, 7174/786?
Answer: GCF of Numerators as per given numbers 544/414, 7174/786 is
GCF of Numerators i.e. for 544,7174 is 34
LCM of denominators i.e. for 414,786 is 54234.
Thus, GCF of Fractions is 34/54234.Finally, GCF of Fractions for 544/414, 7174/786 is 34/54234.