GCF of 586/750, 780/978
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 586/750, 780/978 i.e 2/122250 easily. The following is the detailed procedure to determine the greatest common factor of fractions 586/750, 780/978.
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 586/750,780/978?
Given fractions are 586/750,780/978
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 586/750,780/978, numerators are 586,780
Denominators are 750,978
The GCF of 586,780 is 2 .
LCM of 750,978 is 122250.
The greatest common factor of 586/750,780/978 = [GCF of 586,780]/[LCM of 750,978]= 2/122250
Therefore, the GCF of 586/750,780/978 is 2/122250.
To find the highest common factor of 586,780, we have to find the factors of both numbers and list the highest common factor.
The factors of 586 are 1, 2, 293, 586
The factors of 780 are 1, 2, 3, 4, 5, 6, 10, 12, 13, 15, 20, 26, 30, 39, 52, 60, 65, 78, 130, 156, 195, 260, 390, 780
The HCF of 586,780 is 2.
Lets's calculate GCF of 586,780
| 2 | 586, 780 |
| 293, 390 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 586,780 By Matching Biggest Common Factor Method
Now, list down the factors of 586
:1,2,293,586
Now, list down the factors of 780
:1,2,3,4,5,6,10,12,13,15,20,26,30,39,52,60,65,78,130,156,195,260,390,780
Greatest Common Factor
We found the factors 586,780 . The biggest common factor number is the GCF number.
So the greatest common factor 586,780 is 2.
Lets's calculate LCM of 750,978
| 2 | 750, 978 |
| 3 | 375, 489 |
| 125, 163 |
∴ So the LCM of the given numbers is 2 x 3 x 125 x 163 = 122250
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/122250
Therefore, the GCF of Fractions 586/750,780/978 is 2/122250
Least Common Multiple of 750,978 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 750,978 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(750,978) = 6
common factors(in case of two or more numbers have common factors) = 1
GCF(750,978) x common factors =6 x 1 = 6
LCM(750,978) = ( 750 × 978 ) / 6
LCM(750,978) = 733500 / 6
LCM(750,978) = 122250
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FAQs on GCF of Fractions of 586/750, 780/978
1. What is the HCF of 586,780?
The HCF of 586,780 is 2
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 586/750, 780/978?
Answer: GCF of Numerators as per given numbers 586/750, 780/978 is
GCF of Numerators i.e. for 586,780 is 2
LCM of denominators i.e. for 750,978 is 122250.
Thus, GCF of Fractions is 2/122250.Finally, GCF of Fractions for 586/750, 780/978 is 2/122250.