GCF of 204/778, 321/782
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 204/778, 321/782 i.e 3/304198 easily. The following is the detailed procedure to determine the greatest common factor of fractions 204/778, 321/782.
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 204/778,321/782?
Given fractions are 204/778,321/782
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 204/778,321/782, numerators are 204,321
Denominators are 778,782
The GCF of 204,321 is 3 .
LCM of 778,782 is 304198.
The greatest common factor of 204/778,321/782 = [GCF of 204,321]/[LCM of 778,782]= 3/304198
Therefore, the GCF of 204/778,321/782 is 3/304198.
To find the highest common factor of 204,321, we have to find the factors of both numbers and list the highest common factor.
The factors of 204 are 1, 2, 3, 4, 6, 12, 17, 34, 51, 68, 102, 204
The factors of 321 are 1, 3, 107, 321
The HCF of 204,321 is 3.
Lets's calculate GCF of 204,321
| 3 | 204, 321 |
| 68, 107 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 204,321 By Matching Biggest Common Factor Method
Now, list down the factors of 204
:1,2,3,4,6,12,17,34,51,68,102,204
Now, list down the factors of 321
:1,3,107,321
Greatest Common Factor
We found the factors 204,321 . The biggest common factor number is the GCF number.
So the greatest common factor 204,321 is 3.
Lets's calculate LCM of 778,782
| 2 | 778, 782 |
| 389, 391 |
∴ So the LCM of the given numbers is 2 x 389 x 391 = 304198
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/304198
Therefore, the GCF of Fractions 204/778,321/782 is 3/304198
Least Common Multiple of 778,782 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 778,782 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(778,782) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(778,782) x common factors =2 x 1 = 2
LCM(778,782) = ( 778 × 782 ) / 2
LCM(778,782) = 608396 / 2
LCM(778,782) = 304198
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FAQs on GCF of Fractions of 204/778, 321/782
1. What is the HCF of 204,321?
The HCF of 204,321 is 3
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 204/778, 321/782?
Answer: GCF of Numerators as per given numbers 204/778, 321/782 is
GCF of Numerators i.e. for 204,321 is 3
LCM of denominators i.e. for 778,782 is 304198.
Thus, GCF of Fractions is 3/304198.Finally, GCF of Fractions for 204/778, 321/782 is 3/304198.