GCF of 1730/235, 8580/4084
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1730/235, 8580/4084 i.e 10/959740 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1730/235, 8580/4084.
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 1730/235,8580/4084?
Given fractions are 1730/235,8580/4084
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 1730/235,8580/4084, numerators are 1730,8580
Denominators are 235,4084
The GCF of 1730,8580 is 10 .
LCM of 235,4084 is 959740.
The greatest common factor of 1730/235,8580/4084 = [GCF of 1730,8580]/[LCM of 235,4084]= 10/959740
Therefore, the GCF of 1730/235,8580/4084 is 10/959740.
To find the highest common factor of 1730,8580, we have to find the factors of both numbers and list the highest common factor.
The factors of 1730 are 1, 2, 5, 10, 173, 346, 865, 1730
The factors of 8580 are 1, 2, 3, 4, 5, 6, 10, 11, 12, 13, 15, 20, 22, 26, 30, 33, 39, 44, 52, 55, 60, 65, 66, 78, 110, 130, 132, 143, 156, 165, 195, 220, 260, 286, 330, 390, 429, 572, 660, 715, 780, 858, 1430, 1716, 2145, 2860, 4290, 8580
The HCF of 1730,8580 is 10.
Lets's calculate GCF of 1730,8580
| 2 | 1730, 8580 |
| 5 | 865, 4290 |
| 173, 858 |
∴ So the GCF of the given numbers is 2 x 5 = 10
Greatest Common Factor of 1730,8580 By Matching Biggest Common Factor Method
Now, list down the factors of 1730
:1,2,5,10,173,346,865,1730
Now, list down the factors of 8580
:1,2,3,4,5,6,10,11,12,13,15,20,22,26,30,33,39,44,52,55,60,65,66,78,110,130,132,143,156,165,195,220,260,286,330,390,429,572,660,715,780,858,1430,1716,2145,2860,4290,8580
Greatest Common Factor
We found the factors 1730,8580 . The biggest common factor number is the GCF number.
So the greatest common factor 1730,8580 is 10.
Lets's calculate LCM of 235,4084
Given numbers has no common factors except 1. So, there LCM is their product i.e 959740
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 10/959740
Therefore, the GCF of Fractions 1730/235,8580/4084 is 10/959740
Least Common Multiple of 235,4084 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 235,4084 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(235,4084) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(235,4084) x common factors =1 x 1 = 1
LCM(235,4084) = ( 235 × 4084 ) / 1
LCM(235,4084) = 959740 / 1
LCM(235,4084) = 959740
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FAQs on GCF of Fractions of 1730/235, 8580/4084
1. What is the HCF of 1730,8580?
The HCF of 1730,8580 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 1730/235, 8580/4084?
Answer: GCF of Numerators as per given numbers 1730/235, 8580/4084 is
GCF of Numerators i.e. for 1730,8580 is 10
LCM of denominators i.e. for 235,4084 is 959740.
Thus, GCF of Fractions is 10/959740.Finally, GCF of Fractions for 1730/235, 8580/4084 is 10/959740.