GCF of 299/30, 368/706
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 299/30, 368/706 i.e 23/10590 easily. The following is the detailed procedure to determine the greatest common factor of fractions 299/30, 368/706.
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 299/30,368/706?
Given fractions are 299/30,368/706
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 299/30,368/706, numerators are 299,368
Denominators are 30,706
The GCF of 299,368 is 23 .
LCM of 30,706 is 10590.
The greatest common factor of 299/30,368/706 = [GCF of 299,368]/[LCM of 30,706]= 23/10590
Therefore, the GCF of 299/30,368/706 is 23/10590.
To find the highest common factor of 299,368, we have to find the factors of both numbers and list the highest common factor.
The factors of 299 are 1, 13, 23, 299
The factors of 368 are 1, 2, 4, 8, 16, 23, 46, 92, 184, 368
The HCF of 299,368 is 23.
Lets's calculate GCF of 299,368
| 23 | 299, 368 |
| 13, 16 |
∴ So the GCF of the given numbers is 23 = 23
Greatest Common Factor of 299,368 By Matching Biggest Common Factor Method
Now, list down the factors of 299
:1,13,23,299
Now, list down the factors of 368
:1,2,4,8,16,23,46,92,184,368
Greatest Common Factor
We found the factors 299,368 . The biggest common factor number is the GCF number.
So the greatest common factor 299,368 is 23.
Lets's calculate LCM of 30,706
| 2 | 30, 706 |
| 15, 353 |
∴ So the LCM of the given numbers is 2 x 15 x 353 = 10590
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 23/10590
Therefore, the GCF of Fractions 299/30,368/706 is 23/10590
Least Common Multiple of 30,706 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 30,706 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(30,706) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(30,706) x common factors =2 x 1 = 2
LCM(30,706) = ( 30 × 706 ) / 2
LCM(30,706) = 21180 / 2
LCM(30,706) = 10590
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FAQs on GCF of Fractions of 299/30, 368/706
1. What is the HCF of 299,368?
The HCF of 299,368 is 23
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 299/30, 368/706?
Answer: GCF of Numerators as per given numbers 299/30, 368/706 is
GCF of Numerators i.e. for 299,368 is 23
LCM of denominators i.e. for 30,706 is 10590.
Thus, GCF of Fractions is 23/10590.Finally, GCF of Fractions for 299/30, 368/706 is 23/10590.