GCF of 730/23, 705/124
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 730/23, 705/124 i.e 5/2852 easily. The following is the detailed procedure to determine the greatest common factor of fractions 730/23, 705/124.
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 730/23,705/124?
Given fractions are 730/23,705/124
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 730/23,705/124, numerators are 730,705
Denominators are 23,124
The GCF of 730,705 is 5 .
LCM of 23,124 is 2852.
The greatest common factor of 730/23,705/124 = [GCF of 730,705]/[LCM of 23,124]= 5/2852
Therefore, the GCF of 730/23,705/124 is 5/2852.
To find the highest common factor of 730,705, we have to find the factors of both numbers and list the highest common factor.
The factors of 730 are 1, 2, 5, 10, 73, 146, 365, 730
The factors of 705 are 1, 3, 5, 15, 47, 141, 235, 705
The HCF of 730,705 is 5.
Lets's calculate GCF of 730,705
| 5 | 730, 705 |
| 146, 141 |
∴ So the GCF of the given numbers is 5 = 5
Greatest Common Factor of 730,705 By Matching Biggest Common Factor Method
Now, list down the factors of 730
:1,2,5,10,73,146,365,730
Now, list down the factors of 705
:1,3,5,15,47,141,235,705
Greatest Common Factor
We found the factors 730,705 . The biggest common factor number is the GCF number.
So the greatest common factor 730,705 is 5.
Lets's calculate LCM of 23,124
Given numbers has no common factors except 1. So, there LCM is their product i.e 2852
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 5/2852
Therefore, the GCF of Fractions 730/23,705/124 is 5/2852
Least Common Multiple of 23,124 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 23,124 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(23,124) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(23,124) x common factors =1 x 1 = 1
LCM(23,124) = ( 23 × 124 ) / 1
LCM(23,124) = 2852 / 1
LCM(23,124) = 2852
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FAQs on GCF of Fractions of 730/23, 705/124
1. What is the HCF of 730,705?
The HCF of 730,705 is 5
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 730/23, 705/124?
Answer: GCF of Numerators as per given numbers 730/23, 705/124 is
GCF of Numerators i.e. for 730,705 is 5
LCM of denominators i.e. for 23,124 is 2852.
Thus, GCF of Fractions is 5/2852.Finally, GCF of Fractions for 730/23, 705/124 is 5/2852.