GCF of 206/768, 6142/3680
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 206/768, 6142/3680 i.e 2/88320 easily. The following is the detailed procedure to determine the greatest common factor of fractions 206/768, 6142/3680.
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 206/768,6142/3680?
Given fractions are 206/768,6142/3680
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 206/768,6142/3680, numerators are 206,6142
Denominators are 768,3680
The GCF of 206,6142 is 2 .
LCM of 768,3680 is 88320.
The greatest common factor of 206/768,6142/3680 = [GCF of 206,6142]/[LCM of 768,3680]= 2/88320
Therefore, the GCF of 206/768,6142/3680 is 2/88320.
To find the highest common factor of 206,6142, we have to find the factors of both numbers and list the highest common factor.
The factors of 206 are 1, 2, 103, 206
The factors of 6142 are 1, 2, 37, 74, 83, 166, 3071, 6142
The HCF of 206,6142 is 2.
Lets's calculate GCF of 206,6142
| 2 | 206, 6142 |
| 103, 3071 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 206,6142 By Matching Biggest Common Factor Method
Now, list down the factors of 206
:1,2,103,206
Now, list down the factors of 6142
:1,2,37,74,83,166,3071,6142
Greatest Common Factor
We found the factors 206,6142 . The biggest common factor number is the GCF number.
So the greatest common factor 206,6142 is 2.
Lets's calculate LCM of 768,3680
| 2 | 768, 3680 |
| 2 | 384, 1840 |
| 2 | 192, 920 |
| 2 | 96, 460 |
| 2 | 48, 230 |
| 24, 115 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 2 x 2 x 24 x 115 = 88320
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/88320
Therefore, the GCF of Fractions 206/768,6142/3680 is 2/88320
Least Common Multiple of 768,3680 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 768,3680 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(768,3680) = 32
common factors(in case of two or more numbers have common factors) = 1
GCF(768,3680) x common factors =32 x 1 = 32
LCM(768,3680) = ( 768 × 3680 ) / 32
LCM(768,3680) = 2826240 / 32
LCM(768,3680) = 88320
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FAQs on GCF of Fractions of 206/768, 6142/3680
1. What is the HCF of 206,6142?
The HCF of 206,6142 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 206/768, 6142/3680?
Answer: GCF of Numerators as per given numbers 206/768, 6142/3680 is
GCF of Numerators i.e. for 206,6142 is 2
LCM of denominators i.e. for 768,3680 is 88320.
Thus, GCF of Fractions is 2/88320.Finally, GCF of Fractions for 206/768, 6142/3680 is 2/88320.