GCF of 735/231, 120/674
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 735/231, 120/674 i.e 15/155694 easily. The following is the detailed procedure to determine the greatest common factor of fractions 735/231, 120/674.
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 735/231,120/674?
Given fractions are 735/231,120/674
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 735/231,120/674, numerators are 735,120
Denominators are 231,674
The GCF of 735,120 is 15 .
LCM of 231,674 is 155694.
The greatest common factor of 735/231,120/674 = [GCF of 735,120]/[LCM of 231,674]= 15/155694
Therefore, the GCF of 735/231,120/674 is 15/155694.
To find the highest common factor of 735,120, we have to find the factors of both numbers and list the highest common factor.
The factors of 735 are 1, 3, 5, 7, 15, 21, 35, 49, 105, 147, 245, 735
The factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
The HCF of 735,120 is 15.
Lets's calculate GCF of 735,120
| 3 | 735, 120 |
| 5 | 245, 40 |
| 49, 8 |
∴ So the GCF of the given numbers is 3 x 5 = 15
Greatest Common Factor of 735,120 By Matching Biggest Common Factor Method
Now, list down the factors of 735
:1,3,5,7,15,21,35,49,105,147,245,735
Now, list down the factors of 120
:1,2,3,4,5,6,8,10,12,15,20,24,30,40,60,120
Greatest Common Factor
We found the factors 735,120 . The biggest common factor number is the GCF number.
So the greatest common factor 735,120 is 15.
Lets's calculate LCM of 231,674
Given numbers has no common factors except 1. So, there LCM is their product i.e 155694
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 15/155694
Therefore, the GCF of Fractions 735/231,120/674 is 15/155694
Least Common Multiple of 231,674 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 231,674 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(231,674) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(231,674) x common factors =1 x 1 = 1
LCM(231,674) = ( 231 × 674 ) / 1
LCM(231,674) = 155694 / 1
LCM(231,674) = 155694
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FAQs on GCF of Fractions of 735/231, 120/674
1. What is the HCF of 735,120?
The HCF of 735,120 is 15
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 735/231, 120/674?
Answer: GCF of Numerators as per given numbers 735/231, 120/674 is
GCF of Numerators i.e. for 735,120 is 15
LCM of denominators i.e. for 231,674 is 155694.
Thus, GCF of Fractions is 15/155694.Finally, GCF of Fractions for 735/231, 120/674 is 15/155694.