GCF of 775/306, 590/282
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 775/306, 590/282 i.e 5/14382 easily. The following is the detailed procedure to determine the greatest common factor of fractions 775/306, 590/282.
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 775/306,590/282?
Given fractions are 775/306,590/282
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 775/306,590/282, numerators are 775,590
Denominators are 306,282
The GCF of 775,590 is 5 .
LCM of 306,282 is 14382.
The greatest common factor of 775/306,590/282 = [GCF of 775,590]/[LCM of 306,282]= 5/14382
Therefore, the GCF of 775/306,590/282 is 5/14382.
To find the highest common factor of 775,590, we have to find the factors of both numbers and list the highest common factor.
The factors of 775 are 1, 5, 25, 31, 155, 775
The factors of 590 are 1, 2, 5, 10, 59, 118, 295, 590
The HCF of 775,590 is 5.
Lets's calculate GCF of 775,590
| 5 | 775, 590 |
| 155, 118 |
∴ So the GCF of the given numbers is 5 = 5
Greatest Common Factor of 775,590 By Matching Biggest Common Factor Method
Now, list down the factors of 775
:1,5,25,31,155,775
Now, list down the factors of 590
:1,2,5,10,59,118,295,590
Greatest Common Factor
We found the factors 775,590 . The biggest common factor number is the GCF number.
So the greatest common factor 775,590 is 5.
Lets's calculate LCM of 306,282
| 2 | 306, 282 |
| 3 | 153, 141 |
| 51, 47 |
∴ So the LCM of the given numbers is 2 x 3 x 51 x 47 = 14382
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 5/14382
Therefore, the GCF of Fractions 775/306,590/282 is 5/14382
Least Common Multiple of 306,282 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 306,282 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(306,282) = 6
common factors(in case of two or more numbers have common factors) = 1
GCF(306,282) x common factors =6 x 1 = 6
LCM(306,282) = ( 306 × 282 ) / 6
LCM(306,282) = 86292 / 6
LCM(306,282) = 14382
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FAQs on GCF of Fractions of 775/306, 590/282
1. What is the HCF of 775,590?
The HCF of 775,590 is 5
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 775/306, 590/282?
Answer: GCF of Numerators as per given numbers 775/306, 590/282 is
GCF of Numerators i.e. for 775,590 is 5
LCM of denominators i.e. for 306,282 is 14382.
Thus, GCF of Fractions is 5/14382.Finally, GCF of Fractions for 775/306, 590/282 is 5/14382.