GCF of 34/814, 104/266, 656/209
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 34/814, 104/266, 656/209 i.e 2/108262 easily. The following is the detailed procedure to determine the greatest common factor of fractions 34/814, 104/266, 656/209.
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 34/814,104/266,656/209?
Given fractions are 34/814,104/266,656/209
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 34/814,104/266,656/209, numerators are 34,104,656
Denominators are 814,266,209
The GCF of 34,104,656 is 2 .
LCM of 814,266,209 is 108262.
The greatest common factor of 34/814,104/266,656/209 = [GCF of 34,104,656]/[LCM of 814,266,209]= 2/108262
Therefore, the GCF of 34/814,104/266,656/209 is 2/108262.
To find the highest common factor of 34,104,656, we have to find the factors of both numbers and list the highest common factor.
The factors of 34 are 1, 2, 17, 34
The factors of 104 are 1, 2, 4, 8, 13, 26, 52, 104
The factors of 656 are 1, 2, 4, 8, 16, 41, 82, 164, 328, 656
The HCF of 34,104,656 is 2.
Lets's calculate GCF of 34,104,656
| 2 | 34, 104, 656 |
| 17, 52, 328 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 34,104,656 By Matching Biggest Common Factor Method
Now, list down the factors of 34
:1,2,17,34
Now, list down the factors of 104
:1,2,4,8,13,26,52,104
Now, list down the factors of 656
:1,2,4,8,16,41,82,164,328,656
Greatest Common Factor
We found the factors 34,104,656 . The biggest common factor number is the GCF number.
So the greatest common factor 34,104,656 is 2.
Lets's calculate LCM of 814,266,209
| 2 | 814, 266, 209 |
| 11 | 407, 133, 209 |
| 19 | 37, 133, 19 |
| 37, 7, 1 |
∴ So the LCM of the given numbers is 2 x 11 x 19 x 37 x 7 x 1 = 108262
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/108262
Therefore, the GCF of Fractions 34/814,104/266,656/209 is 2/108262
Least Common Multiple of 814,266,209 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 814,266,209 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(814,266,209) = 1
common factors(in case of two or more numbers have common factors) = 418
GCF(814,266,209) x common factors =1 x 418 = 418
LCM(814,266,209) = ( 814 × 266 × 209 ) / 418
LCM(814,266,209) = 45253516 / 418
LCM(814,266,209) = 108262
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FAQs on GCF of Fractions of 34/814, 104/266, 656/209
1. What is the HCF of 34,104,656?
The HCF of 34,104,656 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 34/814, 104/266, 656/209?
Answer: GCF of Numerators as per given numbers 34/814, 104/266, 656/209 is
GCF of Numerators i.e. for 34,104,656 is 2
LCM of denominators i.e. for 814,266,209 is 108262.
Thus, GCF of Fractions is 2/108262.Finally, GCF of Fractions for 34/814, 104/266, 656/209 is 2/108262.