GCF of 1430/409, 1482/1520
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1430/409, 1482/1520 i.e 26/621680 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1430/409, 1482/1520.
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 1430/409,1482/1520?
Given fractions are 1430/409,1482/1520
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 1430/409,1482/1520, numerators are 1430,1482
Denominators are 409,1520
The GCF of 1430,1482 is 26 .
LCM of 409,1520 is 621680.
The greatest common factor of 1430/409,1482/1520 = [GCF of 1430,1482]/[LCM of 409,1520]= 26/621680
Therefore, the GCF of 1430/409,1482/1520 is 26/621680.
To find the highest common factor of 1430,1482, we have to find the factors of both numbers and list the highest common factor.
The factors of 1430 are 1, 2, 5, 10, 11, 13, 22, 26, 55, 65, 110, 130, 143, 286, 715, 1430
The factors of 1482 are 1, 2, 3, 6, 13, 19, 26, 38, 39, 57, 78, 114, 247, 494, 741, 1482
The HCF of 1430,1482 is 26.
Lets's calculate GCF of 1430,1482
| 2 | 1430, 1482 |
| 13 | 715, 741 |
| 55, 57 |
∴ So the GCF of the given numbers is 2 x 13 = 26
Greatest Common Factor of 1430,1482 By Matching Biggest Common Factor Method
Now, list down the factors of 1430
:1,2,5,10,11,13,22,26,55,65,110,130,143,286,715,1430
Now, list down the factors of 1482
:1,2,3,6,13,19,26,38,39,57,78,114,247,494,741,1482
Greatest Common Factor
We found the factors 1430,1482 . The biggest common factor number is the GCF number.
So the greatest common factor 1430,1482 is 26.
Lets's calculate LCM of 409,1520
Given numbers has no common factors except 1. So, there LCM is their product i.e 621680
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 26/621680
Therefore, the GCF of Fractions 1430/409,1482/1520 is 26/621680
Least Common Multiple of 409,1520 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 409,1520 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(409,1520) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(409,1520) x common factors =1 x 1 = 1
LCM(409,1520) = ( 409 × 1520 ) / 1
LCM(409,1520) = 621680 / 1
LCM(409,1520) = 621680
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FAQs on GCF of Fractions of 1430/409, 1482/1520
1. What is the HCF of 1430,1482?
The HCF of 1430,1482 is 26
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 1430/409, 1482/1520?
Answer: GCF of Numerators as per given numbers 1430/409, 1482/1520 is
GCF of Numerators i.e. for 1430,1482 is 26
LCM of denominators i.e. for 409,1520 is 621680.
Thus, GCF of Fractions is 26/621680.Finally, GCF of Fractions for 1430/409, 1482/1520 is 26/621680.