GCF of 75/81, 98/76, 420/580
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 75/81, 98/76, 420/580 i.e 1/892620 easily. The following is the detailed procedure to determine the greatest common factor of fractions 75/81, 98/76, 420/580.
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 75/81,98/76,420/580?
Given fractions are 75/81,98/76,420/580
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 75/81,98/76,420/580, numerators are 75,98,420
Denominators are 81,76,580
The GCF of 75,98,420 is 1 .
LCM of 81,76,580 is 892620.
The greatest common factor of 75/81,98/76,420/580 = [GCF of 75,98,420]/[LCM of 81,76,580]= 1/892620
Therefore, the GCF of 75/81,98/76,420/580 is 1/892620.
To find the highest common factor of 75,98,420, we have to find the factors of both numbers and list the highest common factor.
The factors of 75 are 1, 3, 5, 15, 25, 75
The factors of 98 are 1, 2, 7, 14, 49, 98
The factors of 420 are 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, 420
The HCF of 75,98,420 is 1.
Lets's calculate GCF of 75,98,420
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 75,98,420 By Matching Biggest Common Factor Method
Now, list down the factors of 75
:1,3,5,15,25,75
Now, list down the factors of 98
:1,2,7,14,49,98
Now, list down the factors of 420
:1,2,3,4,5,6,7,10,12,14,15,20,21,28,30,35,42,60,70,84,105,140,210,420
Greatest Common Factor
We found the factors 75,98,420 . The biggest common factor number is the GCF number.
So the greatest common factor 75,98,420 is 1.
Lets's calculate LCM of 81,76,580
| 2 | 81, 76, 580 |
| 2 | 81, 38, 290 |
| 81, 19, 145 |
∴ So the LCM of the given numbers is 2 x 2 x 81 x 19 x 145 = 892620
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/892620
Therefore, the GCF of Fractions 75/81,98/76,420/580 is 1/892620
Least Common Multiple of 81,76,580 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 81,76,580 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(81,76,580) = 1
common factors(in case of two or more numbers have common factors) = 4
GCF(81,76,580) x common factors =1 x 4 = 4
LCM(81,76,580) = ( 81 × 76 × 580 ) / 4
LCM(81,76,580) = 3570480 / 4
LCM(81,76,580) = 892620
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FAQs on GCF of Fractions of 75/81, 98/76, 420/580
1. What is the HCF of 75,98,420?
The HCF of 75,98,420 is 1
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 75/81, 98/76, 420/580?
Answer: GCF of Numerators as per given numbers 75/81, 98/76, 420/580 is
GCF of Numerators i.e. for 75,98,420 is 1
LCM of denominators i.e. for 81,76,580 is 892620.
Thus, GCF of Fractions is 1/892620.Finally, GCF of Fractions for 75/81, 98/76, 420/580 is 1/892620.