GCF of 856/85, 780/82, 774/74
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 856/85, 780/82, 774/74 i.e 2/257890 easily. The following is the detailed procedure to determine the greatest common factor of fractions 856/85, 780/82, 774/74.
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 856/85,780/82,774/74?
Given fractions are 856/85,780/82,774/74
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 856/85,780/82,774/74, numerators are 856,780,774
Denominators are 85,82,74
The GCF of 856,780,774 is 2 .
LCM of 85,82,74 is 257890.
The greatest common factor of 856/85,780/82,774/74 = [GCF of 856,780,774]/[LCM of 85,82,74]= 2/257890
Therefore, the GCF of 856/85,780/82,774/74 is 2/257890.
To find the highest common factor of 856,780,774, we have to find the factors of both numbers and list the highest common factor.
The factors of 856 are 1, 2, 4, 8, 107, 214, 428, 856
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 factors of 774 are 1, 2, 3, 6, 9, 18, 43, 86, 129, 258, 387, 774
The HCF of 856,780,774 is 2.
Lets's calculate GCF of 856,780,774
| 2 | 856, 780, 774 |
| 428, 390, 387 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 856,780,774 By Matching Biggest Common Factor Method
Now, list down the factors of 856
:1,2,4,8,107,214,428,856
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
Now, list down the factors of 774
:1,2,3,6,9,18,43,86,129,258,387,774
Greatest Common Factor
We found the factors 856,780,774 . The biggest common factor number is the GCF number.
So the greatest common factor 856,780,774 is 2.
Lets's calculate LCM of 85,82,74
| 2 | 85, 82, 74 |
| 85, 41, 37 |
∴ So the LCM of the given numbers is 2 x 85 x 41 x 37 = 257890
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/257890
Therefore, the GCF of Fractions 856/85,780/82,774/74 is 2/257890
Least Common Multiple of 85,82,74 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 85,82,74 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(85,82,74) = 1
common factors(in case of two or more numbers have common factors) = 2
GCF(85,82,74) x common factors =1 x 2 = 2
LCM(85,82,74) = ( 85 × 82 × 74 ) / 2
LCM(85,82,74) = 515780 / 2
LCM(85,82,74) = 257890
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 856/85, 780/82, 774/74
1. What is the HCF of 856,780,774?
The HCF of 856,780,774 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 856/85, 780/82, 774/74?
Answer: GCF of Numerators as per given numbers 856/85, 780/82, 774/74 is
GCF of Numerators i.e. for 856,780,774 is 2
LCM of denominators i.e. for 85,82,74 is 257890.
Thus, GCF of Fractions is 2/257890.Finally, GCF of Fractions for 856/85, 780/82, 774/74 is 2/257890.