GCF of 1430/175, 6580/7494
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1430/175, 6580/7494 i.e 10/1311450 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1430/175, 6580/7494.
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 1430/175,6580/7494?
Given fractions are 1430/175,6580/7494
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 1430/175,6580/7494, numerators are 1430,6580
Denominators are 175,7494
The GCF of 1430,6580 is 10 .
LCM of 175,7494 is 1311450.
The greatest common factor of 1430/175,6580/7494 = [GCF of 1430,6580]/[LCM of 175,7494]= 10/1311450
Therefore, the GCF of 1430/175,6580/7494 is 10/1311450.
To find the highest common factor of 1430,6580, 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 6580 are 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 47, 70, 94, 140, 188, 235, 329, 470, 658, 940, 1316, 1645, 3290, 6580
The HCF of 1430,6580 is 10.
Lets's calculate GCF of 1430,6580
| 2 | 1430, 6580 |
| 5 | 715, 3290 |
| 143, 658 |
∴ So the GCF of the given numbers is 2 x 5 = 10
Greatest Common Factor of 1430,6580 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 6580
:1,2,4,5,7,10,14,20,28,35,47,70,94,140,188,235,329,470,658,940,1316,1645,3290,6580
Greatest Common Factor
We found the factors 1430,6580 . The biggest common factor number is the GCF number.
So the greatest common factor 1430,6580 is 10.
Lets's calculate LCM of 175,7494
Given numbers has no common factors except 1. So, there LCM is their product i.e 1311450
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 10/1311450
Therefore, the GCF of Fractions 1430/175,6580/7494 is 10/1311450
Least Common Multiple of 175,7494 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 175,7494 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(175,7494) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(175,7494) x common factors =1 x 1 = 1
LCM(175,7494) = ( 175 × 7494 ) / 1
LCM(175,7494) = 1311450 / 1
LCM(175,7494) = 1311450
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FAQs on GCF of Fractions of 1430/175, 6580/7494
1. What is the HCF of 1430,6580?
The HCF of 1430,6580 is 10
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 1430/175, 6580/7494?
Answer: GCF of Numerators as per given numbers 1430/175, 6580/7494 is
GCF of Numerators i.e. for 1430,6580 is 10
LCM of denominators i.e. for 175,7494 is 1311450.
Thus, GCF of Fractions is 10/1311450.Finally, GCF of Fractions for 1430/175, 6580/7494 is 10/1311450.