GCF of 1230/280, 1574/760
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1230/280, 1574/760 i.e 2/5320 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1230/280, 1574/760.
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 1230/280,1574/760?
Given fractions are 1230/280,1574/760
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 1230/280,1574/760, numerators are 1230,1574
Denominators are 280,760
The GCF of 1230,1574 is 2 .
LCM of 280,760 is 5320.
The greatest common factor of 1230/280,1574/760 = [GCF of 1230,1574]/[LCM of 280,760]= 2/5320
Therefore, the GCF of 1230/280,1574/760 is 2/5320.
To find the highest common factor of 1230,1574, we have to find the factors of both numbers and list the highest common factor.
The factors of 1230 are 1, 2, 3, 5, 6, 10, 15, 30, 41, 82, 123, 205, 246, 410, 615, 1230
The factors of 1574 are 1, 2, 787, 1574
The HCF of 1230,1574 is 2.
Lets's calculate GCF of 1230,1574
| 2 | 1230, 1574 |
| 615, 787 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 1230,1574 By Matching Biggest Common Factor Method
Now, list down the factors of 1230
:1,2,3,5,6,10,15,30,41,82,123,205,246,410,615,1230
Now, list down the factors of 1574
:1,2,787,1574
Greatest Common Factor
We found the factors 1230,1574 . The biggest common factor number is the GCF number.
So the greatest common factor 1230,1574 is 2.
Lets's calculate LCM of 280,760
| 2 | 280, 760 |
| 2 | 140, 380 |
| 2 | 70, 190 |
| 5 | 35, 95 |
| 7, 19 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 5 x 7 x 19 = 5320
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/5320
Therefore, the GCF of Fractions 1230/280,1574/760 is 2/5320
Least Common Multiple of 280,760 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 280,760 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(280,760) = 40
common factors(in case of two or more numbers have common factors) = 1
GCF(280,760) x common factors =40 x 1 = 40
LCM(280,760) = ( 280 × 760 ) / 40
LCM(280,760) = 212800 / 40
LCM(280,760) = 5320
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FAQs on GCF of Fractions of 1230/280, 1574/760
1. What is the HCF of 1230,1574?
The HCF of 1230,1574 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 1230/280, 1574/760?
Answer: GCF of Numerators as per given numbers 1230/280, 1574/760 is
GCF of Numerators i.e. for 1230,1574 is 2
LCM of denominators i.e. for 280,760 is 5320.
Thus, GCF of Fractions is 2/5320.Finally, GCF of Fractions for 1230/280, 1574/760 is 2/5320.