GCF of 100/678, 5474/741
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 100/678, 5474/741 i.e 2/167466 easily. The following is the detailed procedure to determine the greatest common factor of fractions 100/678, 5474/741.
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 100/678,5474/741?
Given fractions are 100/678,5474/741
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 100/678,5474/741, numerators are 100,5474
Denominators are 678,741
The GCF of 100,5474 is 2 .
LCM of 678,741 is 167466.
The greatest common factor of 100/678,5474/741 = [GCF of 100,5474]/[LCM of 678,741]= 2/167466
Therefore, the GCF of 100/678,5474/741 is 2/167466.
To find the highest common factor of 100,5474, we have to find the factors of both numbers and list the highest common factor.
The factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, 100
The factors of 5474 are 1, 2, 7, 14, 17, 23, 34, 46, 119, 161, 238, 322, 391, 782, 2737, 5474
The HCF of 100,5474 is 2.
Lets's calculate GCF of 100,5474
| 2 | 100, 5474 |
| 50, 2737 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 100,5474 By Matching Biggest Common Factor Method
Now, list down the factors of 100
:1,2,4,5,10,20,25,50,100
Now, list down the factors of 5474
:1,2,7,14,17,23,34,46,119,161,238,322,391,782,2737,5474
Greatest Common Factor
We found the factors 100,5474 . The biggest common factor number is the GCF number.
So the greatest common factor 100,5474 is 2.
Lets's calculate LCM of 678,741
| 3 | 678, 741 |
| 226, 247 |
∴ So the LCM of the given numbers is 3 x 226 x 247 = 167466
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/167466
Therefore, the GCF of Fractions 100/678,5474/741 is 2/167466
Least Common Multiple of 678,741 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 678,741 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(678,741) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(678,741) x common factors =3 x 1 = 3
LCM(678,741) = ( 678 × 741 ) / 3
LCM(678,741) = 502398 / 3
LCM(678,741) = 167466
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FAQs on GCF of Fractions of 100/678, 5474/741
1. What is the HCF of 100,5474?
The HCF of 100,5474 is 2
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 100/678, 5474/741?
Answer: GCF of Numerators as per given numbers 100/678, 5474/741 is
GCF of Numerators i.e. for 100,5474 is 2
LCM of denominators i.e. for 678,741 is 167466.
Thus, GCF of Fractions is 2/167466.Finally, GCF of Fractions for 100/678, 5474/741 is 2/167466.