GCF of 17/344, 71/266, 382/728
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 17/344, 71/266, 382/728 i.e 1/594776 easily. The following is the detailed procedure to determine the greatest common factor of fractions 17/344, 71/266, 382/728.
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 17/344,71/266,382/728?
Given fractions are 17/344,71/266,382/728
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 17/344,71/266,382/728, numerators are 17,71,382
Denominators are 344,266,728
The GCF of 17,71,382 is 1 .
LCM of 344,266,728 is 594776.
The greatest common factor of 17/344,71/266,382/728 = [GCF of 17,71,382]/[LCM of 344,266,728]= 1/594776
Therefore, the GCF of 17/344,71/266,382/728 is 1/594776.
To find the highest common factor of 17,71,382, we have to find the factors of both numbers and list the highest common factor.
The factors of 17 are 1, 17
The factors of 71 are 1, 71
The factors of 382 are 1, 2, 191, 382
The HCF of 17,71,382 is 1.
Lets's calculate GCF of 17,71,382
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 17,71,382 By Matching Biggest Common Factor Method
Now, list down the factors of 17
:1,17
Now, list down the factors of 71
:1,71
Now, list down the factors of 382
:1,2,191,382
Greatest Common Factor
We found the factors 17,71,382 . The biggest common factor number is the GCF number.
So the greatest common factor 17,71,382 is 1.
Lets's calculate LCM of 344,266,728
| 2 | 344, 266, 728 |
| 2 | 172, 133, 364 |
| 2 | 86, 133, 182 |
| 7 | 43, 133, 91 |
| 43, 19, 13 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 7 x 43 x 19 x 13 = 594776
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/594776
Therefore, the GCF of Fractions 17/344,71/266,382/728 is 1/594776
Least Common Multiple of 344,266,728 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 344,266,728 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(344,266,728) = 2
common factors(in case of two or more numbers have common factors) = 56
GCF(344,266,728) x common factors =2 x 56 = 112
LCM(344,266,728) = ( 344 × 266 × 728 ) / 112
LCM(344,266,728) = 66614912 / 112
LCM(344,266,728) = 594776
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FAQs on GCF of Fractions of 17/344, 71/266, 382/728
1. What is the HCF of 17,71,382?
The HCF of 17,71,382 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 17/344, 71/266, 382/728?
Answer: GCF of Numerators as per given numbers 17/344, 71/266, 382/728 is
GCF of Numerators i.e. for 17,71,382 is 1
LCM of denominators i.e. for 344,266,728 is 594776.
Thus, GCF of Fractions is 1/594776.Finally, GCF of Fractions for 17/344, 71/266, 382/728 is 1/594776.