GCF of 849/714, 3234/340
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 849/714, 3234/340 i.e 3/7140 easily. The following is the detailed procedure to determine the greatest common factor of fractions 849/714, 3234/340.
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 849/714,3234/340?
Given fractions are 849/714,3234/340
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 849/714,3234/340, numerators are 849,3234
Denominators are 714,340
The GCF of 849,3234 is 3 .
LCM of 714,340 is 7140.
The greatest common factor of 849/714,3234/340 = [GCF of 849,3234]/[LCM of 714,340]= 3/7140
Therefore, the GCF of 849/714,3234/340 is 3/7140.
To find the highest common factor of 849,3234, we have to find the factors of both numbers and list the highest common factor.
The factors of 849 are 1, 3, 283, 849
The factors of 3234 are 1, 2, 3, 6, 7, 11, 14, 21, 22, 33, 42, 49, 66, 77, 98, 147, 154, 231, 294, 462, 539, 1078, 1617, 3234
The HCF of 849,3234 is 3.
Lets's calculate GCF of 849,3234
| 3 | 849, 3234 |
| 283, 1078 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 849,3234 By Matching Biggest Common Factor Method
Now, list down the factors of 849
:1,3,283,849
Now, list down the factors of 3234
:1,2,3,6,7,11,14,21,22,33,42,49,66,77,98,147,154,231,294,462,539,1078,1617,3234
Greatest Common Factor
We found the factors 849,3234 . The biggest common factor number is the GCF number.
So the greatest common factor 849,3234 is 3.
Lets's calculate LCM of 714,340
| 2 | 714, 340 |
| 17 | 357, 170 |
| 21, 10 |
∴ So the LCM of the given numbers is 2 x 17 x 21 x 10 = 7140
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/7140
Therefore, the GCF of Fractions 849/714,3234/340 is 3/7140
Least Common Multiple of 714,340 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 714,340 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(714,340) = 34
common factors(in case of two or more numbers have common factors) = 1
GCF(714,340) x common factors =34 x 1 = 34
LCM(714,340) = ( 714 × 340 ) / 34
LCM(714,340) = 242760 / 34
LCM(714,340) = 7140
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FAQs on GCF of Fractions of 849/714, 3234/340
1. What is the HCF of 849,3234?
The HCF of 849,3234 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 849/714, 3234/340?
Answer: GCF of Numerators as per given numbers 849/714, 3234/340 is
GCF of Numerators i.e. for 849,3234 is 3
LCM of denominators i.e. for 714,340 is 7140.
Thus, GCF of Fractions is 3/7140.Finally, GCF of Fractions for 849/714, 3234/340 is 3/7140.