GCF of 319/57, 680/72, 786/10
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 319/57, 680/72, 786/10 i.e 1/6840 easily. The following is the detailed procedure to determine the greatest common factor of fractions 319/57, 680/72, 786/10.
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 319/57,680/72,786/10?
Given fractions are 319/57,680/72,786/10
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 319/57,680/72,786/10, numerators are 319,680,786
Denominators are 57,72,10
The GCF of 319,680,786 is 1 .
LCM of 57,72,10 is 6840.
The greatest common factor of 319/57,680/72,786/10 = [GCF of 319,680,786]/[LCM of 57,72,10]= 1/6840
Therefore, the GCF of 319/57,680/72,786/10 is 1/6840.
To find the highest common factor of 319,680,786, we have to find the factors of both numbers and list the highest common factor.
The factors of 319 are 1, 11, 29, 319
The factors of 680 are 1, 2, 4, 5, 8, 10, 17, 20, 34, 40, 68, 85, 136, 170, 340, 680
The factors of 786 are 1, 2, 3, 6, 131, 262, 393, 786
The HCF of 319,680,786 is 1.
Lets's calculate GCF of 319,680,786
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 319,680,786 By Matching Biggest Common Factor Method
Now, list down the factors of 319
:1,11,29,319
Now, list down the factors of 680
:1,2,4,5,8,10,17,20,34,40,68,85,136,170,340,680
Now, list down the factors of 786
:1,2,3,6,131,262,393,786
Greatest Common Factor
We found the factors 319,680,786 . The biggest common factor number is the GCF number.
So the greatest common factor 319,680,786 is 1.
Lets's calculate LCM of 57,72,10
| 2 | 57, 72, 10 |
| 3 | 57, 36, 5 |
| 19, 12, 5 |
∴ So the LCM of the given numbers is 2 x 3 x 19 x 12 x 5 = 6840
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/6840
Therefore, the GCF of Fractions 319/57,680/72,786/10 is 1/6840
Least Common Multiple of 57,72,10 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 57,72,10 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(57,72,10) = 1
common factors(in case of two or more numbers have common factors) = 6
GCF(57,72,10) x common factors =1 x 6 = 6
LCM(57,72,10) = ( 57 × 72 × 10 ) / 6
LCM(57,72,10) = 41040 / 6
LCM(57,72,10) = 6840
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FAQs on GCF of Fractions of 319/57, 680/72, 786/10
1. What is the HCF of 319,680,786?
The HCF of 319,680,786 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 319/57, 680/72, 786/10?
Answer: GCF of Numerators as per given numbers 319/57, 680/72, 786/10 is
GCF of Numerators i.e. for 319,680,786 is 1
LCM of denominators i.e. for 57,72,10 is 6840.
Thus, GCF of Fractions is 1/6840.Finally, GCF of Fractions for 319/57, 680/72, 786/10 is 1/6840.