GCF of 331/36, 176/54, 786/105
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 331/36, 176/54, 786/105 i.e 1/3780 easily. The following is the detailed procedure to determine the greatest common factor of fractions 331/36, 176/54, 786/105.
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 331/36,176/54,786/105?
Given fractions are 331/36,176/54,786/105
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 331/36,176/54,786/105, numerators are 331,176,786
Denominators are 36,54,105
The GCF of 331,176,786 is 1 .
LCM of 36,54,105 is 3780.
The greatest common factor of 331/36,176/54,786/105 = [GCF of 331,176,786]/[LCM of 36,54,105]= 1/3780
Therefore, the GCF of 331/36,176/54,786/105 is 1/3780.
To find the highest common factor of 331,176,786, we have to find the factors of both numbers and list the highest common factor.
The factors of 331 are 1, 331
The factors of 176 are 1, 2, 4, 8, 11, 16, 22, 44, 88, 176
The factors of 786 are 1, 2, 3, 6, 131, 262, 393, 786
The HCF of 331,176,786 is 1.
Lets's calculate GCF of 331,176,786
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 331,176,786 By Matching Biggest Common Factor Method
Now, list down the factors of 331
:1,331
Now, list down the factors of 176
:1,2,4,8,11,16,22,44,88,176
Now, list down the factors of 786
:1,2,3,6,131,262,393,786
Greatest Common Factor
We found the factors 331,176,786 . The biggest common factor number is the GCF number.
So the greatest common factor 331,176,786 is 1.
Lets's calculate LCM of 36,54,105
| 2 | 36, 54, 105 |
| 3 | 18, 27, 105 |
| 3 | 6, 9, 35 |
| 2, 3, 35 |
∴ So the LCM of the given numbers is 2 x 3 x 3 x 2 x 3 x 35 = 3780
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/3780
Therefore, the GCF of Fractions 331/36,176/54,786/105 is 1/3780
Least Common Multiple of 36,54,105 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 36,54,105 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(36,54,105) = 3
common factors(in case of two or more numbers have common factors) = 18
GCF(36,54,105) x common factors =3 x 18 = 54
LCM(36,54,105) = ( 36 × 54 × 105 ) / 54
LCM(36,54,105) = 204120 / 54
LCM(36,54,105) = 3780
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FAQs on GCF of Fractions of 331/36, 176/54, 786/105
1. What is the HCF of 331,176,786?
The HCF of 331,176,786 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 331/36, 176/54, 786/105?
Answer: GCF of Numerators as per given numbers 331/36, 176/54, 786/105 is
GCF of Numerators i.e. for 331,176,786 is 1
LCM of denominators i.e. for 36,54,105 is 3780.
Thus, GCF of Fractions is 1/3780.Finally, GCF of Fractions for 331/36, 176/54, 786/105 is 1/3780.