GCF of 712/765, 782/978, 220/561
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 712/765, 782/978, 220/561 i.e 2/2743290 easily. The following is the detailed procedure to determine the greatest common factor of fractions 712/765, 782/978, 220/561.
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 712/765,782/978,220/561?
Given fractions are 712/765,782/978,220/561
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 712/765,782/978,220/561, numerators are 712,782,220
Denominators are 765,978,561
The GCF of 712,782,220 is 2 .
LCM of 765,978,561 is 2743290.
The greatest common factor of 712/765,782/978,220/561 = [GCF of 712,782,220]/[LCM of 765,978,561]= 2/2743290
Therefore, the GCF of 712/765,782/978,220/561 is 2/2743290.
To find the highest common factor of 712,782,220, we have to find the factors of both numbers and list the highest common factor.
The factors of 712 are 1, 2, 4, 8, 89, 178, 356, 712
The factors of 782 are 1, 2, 17, 23, 34, 46, 391, 782
The factors of 220 are 1, 2, 4, 5, 10, 11, 20, 22, 44, 55, 110, 220
The HCF of 712,782,220 is 2.
Lets's calculate GCF of 712,782,220
| 2 | 712, 782, 220 |
| 356, 391, 110 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 712,782,220 By Matching Biggest Common Factor Method
Now, list down the factors of 712
:1,2,4,8,89,178,356,712
Now, list down the factors of 782
:1,2,17,23,34,46,391,782
Now, list down the factors of 220
:1,2,4,5,10,11,20,22,44,55,110,220
Greatest Common Factor
We found the factors 712,782,220 . The biggest common factor number is the GCF number.
So the greatest common factor 712,782,220 is 2.
Lets's calculate LCM of 765,978,561
| 3 | 765, 978, 561 |
| 17 | 255, 326, 187 |
| 15, 326, 11 |
∴ So the LCM of the given numbers is 3 x 17 x 15 x 326 x 11 = 2743290
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/2743290
Therefore, the GCF of Fractions 712/765,782/978,220/561 is 2/2743290
Least Common Multiple of 765,978,561 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 765,978,561 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(765,978,561) = 3
common factors(in case of two or more numbers have common factors) = 51
GCF(765,978,561) x common factors =3 x 51 = 153
LCM(765,978,561) = ( 765 × 978 × 561 ) / 153
LCM(765,978,561) = 419723370 / 153
LCM(765,978,561) = 2743290
GCF of Fractions Calculation Examples
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FAQs on GCF of Fractions of 712/765, 782/978, 220/561
1. What is the HCF of 712,782,220?
The HCF of 712,782,220 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 712/765, 782/978, 220/561?
Answer: GCF of Numerators as per given numbers 712/765, 782/978, 220/561 is
GCF of Numerators i.e. for 712,782,220 is 2
LCM of denominators i.e. for 765,978,561 is 2743290.
Thus, GCF of Fractions is 2/2743290.Finally, GCF of Fractions for 712/765, 782/978, 220/561 is 2/2743290.