GCF of 73/231, 98/420, 349/825
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 73/231, 98/420, 349/825 i.e 1/23100 easily. The following is the detailed procedure to determine the greatest common factor of fractions 73/231, 98/420, 349/825.
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 73/231,98/420,349/825?
Given fractions are 73/231,98/420,349/825
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 73/231,98/420,349/825, numerators are 73,98,349
Denominators are 231,420,825
The GCF of 73,98,349 is 1 .
LCM of 231,420,825 is 23100.
The greatest common factor of 73/231,98/420,349/825 = [GCF of 73,98,349]/[LCM of 231,420,825]= 1/23100
Therefore, the GCF of 73/231,98/420,349/825 is 1/23100.
To find the highest common factor of 73,98,349, we have to find the factors of both numbers and list the highest common factor.
The factors of 73 are 1, 73
The factors of 98 are 1, 2, 7, 14, 49, 98
The factors of 349 are 1, 349
The HCF of 73,98,349 is 1.
Lets's calculate GCF of 73,98,349
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 73,98,349 By Matching Biggest Common Factor Method
Now, list down the factors of 73
:1,73
Now, list down the factors of 98
:1,2,7,14,49,98
Now, list down the factors of 349
:1,349
Greatest Common Factor
We found the factors 73,98,349 . The biggest common factor number is the GCF number.
So the greatest common factor 73,98,349 is 1.
Lets's calculate LCM of 231,420,825
| 3 | 231, 420, 825 |
| 5 | 77, 140, 275 |
| 7 | 77, 28, 55 |
| 11 | 11, 4, 55 |
| 1, 4, 5 |
∴ So the LCM of the given numbers is 3 x 5 x 7 x 11 x 1 x 4 x 5 = 23100
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/23100
Therefore, the GCF of Fractions 73/231,98/420,349/825 is 1/23100
Least Common Multiple of 231,420,825 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 231,420,825 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(231,420,825) = 3
common factors(in case of two or more numbers have common factors) = 1155
GCF(231,420,825) x common factors =3 x 1155 = 3465
LCM(231,420,825) = ( 231 × 420 × 825 ) / 3465
LCM(231,420,825) = 80041500 / 3465
LCM(231,420,825) = 23100
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FAQs on GCF of Fractions of 73/231, 98/420, 349/825
1. What is the HCF of 73,98,349?
The HCF of 73,98,349 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 73/231, 98/420, 349/825?
Answer: GCF of Numerators as per given numbers 73/231, 98/420, 349/825 is
GCF of Numerators i.e. for 73,98,349 is 1
LCM of denominators i.e. for 231,420,825 is 23100.
Thus, GCF of Fractions is 1/23100.Finally, GCF of Fractions for 73/231, 98/420, 349/825 is 1/23100.