GCF of 749/49, 258/973
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 749/49, 258/973 i.e 1/6811 easily. The following is the detailed procedure to determine the greatest common factor of fractions 749/49, 258/973.
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 749/49,258/973?
Given fractions are 749/49,258/973
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 749/49,258/973, numerators are 749,258
Denominators are 49,973
The GCF of 749,258 is 1 .
LCM of 49,973 is 6811.
The greatest common factor of 749/49,258/973 = [GCF of 749,258]/[LCM of 49,973]= 1/6811
Therefore, the GCF of 749/49,258/973 is 1/6811.
To find the highest common factor of 749,258, we have to find the factors of both numbers and list the highest common factor.
The factors of 749 are 1, 7, 107, 749
The factors of 258 are 1, 2, 3, 6, 43, 86, 129, 258
The HCF of 749,258 is 1.
Lets's calculate GCF of 749,258
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 749,258 By Matching Biggest Common Factor Method
Now, list down the factors of 749
:1,7,107,749
Now, list down the factors of 258
:1,2,3,6,43,86,129,258
Greatest Common Factor
We found the factors 749,258 . The biggest common factor number is the GCF number.
So the greatest common factor 749,258 is 1.
Lets's calculate LCM of 49,973
| 7 | 49, 973 |
| 7, 139 |
∴ So the LCM of the given numbers is 7 x 7 x 139 = 6811
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/6811
Therefore, the GCF of Fractions 749/49,258/973 is 1/6811
Least Common Multiple of 49,973 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 49,973 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(49,973) = 7
common factors(in case of two or more numbers have common factors) = 1
GCF(49,973) x common factors =7 x 1 = 7
LCM(49,973) = ( 49 × 973 ) / 7
LCM(49,973) = 47677 / 7
LCM(49,973) = 6811
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FAQs on GCF of Fractions of 749/49, 258/973
1. What is the HCF of 749,258?
The HCF of 749,258 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 749/49, 258/973?
Answer: GCF of Numerators as per given numbers 749/49, 258/973 is
GCF of Numerators i.e. for 749,258 is 1
LCM of denominators i.e. for 49,973 is 6811.
Thus, GCF of Fractions is 1/6811.Finally, GCF of Fractions for 749/49, 258/973 is 1/6811.