GCF of 204/214, 782/420
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 204/214, 782/420 i.e 34/44940 easily. The following is the detailed procedure to determine the greatest common factor of fractions 204/214, 782/420.
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 204/214,782/420?
Given fractions are 204/214,782/420
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 204/214,782/420, numerators are 204,782
Denominators are 214,420
The GCF of 204,782 is 34 .
LCM of 214,420 is 44940.
The greatest common factor of 204/214,782/420 = [GCF of 204,782]/[LCM of 214,420]= 34/44940
Therefore, the GCF of 204/214,782/420 is 34/44940.
To find the highest common factor of 204,782, 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 782 are 1, 2, 17, 23, 34, 46, 391, 782
The HCF of 204,782 is 34.
Lets's calculate GCF of 204,782
| 2 | 204, 782 |
| 17 | 102, 391 |
| 6, 23 |
∴ So the GCF of the given numbers is 2 x 17 = 34
Greatest Common Factor of 204,782 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 782
:1,2,17,23,34,46,391,782
Greatest Common Factor
We found the factors 204,782 . The biggest common factor number is the GCF number.
So the greatest common factor 204,782 is 34.
Lets's calculate LCM of 214,420
| 2 | 214, 420 |
| 107, 210 |
∴ So the LCM of the given numbers is 2 x 107 x 210 = 44940
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 34/44940
Therefore, the GCF of Fractions 204/214,782/420 is 34/44940
Least Common Multiple of 214,420 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 214,420 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(214,420) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(214,420) x common factors =2 x 1 = 2
LCM(214,420) = ( 214 × 420 ) / 2
LCM(214,420) = 89880 / 2
LCM(214,420) = 44940
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FAQs on GCF of Fractions of 204/214, 782/420
1. What is the HCF of 204,782?
The HCF of 204,782 is 34
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 204/214, 782/420?
Answer: GCF of Numerators as per given numbers 204/214, 782/420 is
GCF of Numerators i.e. for 204,782 is 34
LCM of denominators i.e. for 214,420 is 44940.
Thus, GCF of Fractions is 34/44940.Finally, GCF of Fractions for 204/214, 782/420 is 34/44940.