GCF of 6749/105, 4082/4221
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 6749/105, 4082/4221 i.e 1/21105 easily. The following is the detailed procedure to determine the greatest common factor of fractions 6749/105, 4082/4221.
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 6749/105,4082/4221?
Given fractions are 6749/105,4082/4221
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 6749/105,4082/4221, numerators are 6749,4082
Denominators are 105,4221
The GCF of 6749,4082 is 1 .
LCM of 105,4221 is 21105.
The greatest common factor of 6749/105,4082/4221 = [GCF of 6749,4082]/[LCM of 105,4221]= 1/21105
Therefore, the GCF of 6749/105,4082/4221 is 1/21105.
To find the highest common factor of 6749,4082, we have to find the factors of both numbers and list the highest common factor.
The factors of 6749 are 1, 17, 397, 6749
The factors of 4082 are 1, 2, 13, 26, 157, 314, 2041, 4082
The HCF of 6749,4082 is 1.
Lets's calculate GCF of 6749,4082
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 6749,4082 By Matching Biggest Common Factor Method
Now, list down the factors of 6749
:1,17,397,6749
Now, list down the factors of 4082
:1,2,13,26,157,314,2041,4082
Greatest Common Factor
We found the factors 6749,4082 . The biggest common factor number is the GCF number.
So the greatest common factor 6749,4082 is 1.
Lets's calculate LCM of 105,4221
| 3 | 105, 4221 |
| 7 | 35, 1407 |
| 5, 201 |
∴ So the LCM of the given numbers is 3 x 7 x 5 x 201 = 21105
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/21105
Therefore, the GCF of Fractions 6749/105,4082/4221 is 1/21105
Least Common Multiple of 105,4221 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 105,4221 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(105,4221) = 21
common factors(in case of two or more numbers have common factors) = 1
GCF(105,4221) x common factors =21 x 1 = 21
LCM(105,4221) = ( 105 × 4221 ) / 21
LCM(105,4221) = 443205 / 21
LCM(105,4221) = 21105
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FAQs on GCF of Fractions of 6749/105, 4082/4221
1. What is the HCF of 6749,4082?
The HCF of 6749,4082 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 6749/105, 4082/4221?
Answer: GCF of Numerators as per given numbers 6749/105, 4082/4221 is
GCF of Numerators i.e. for 6749,4082 is 1
LCM of denominators i.e. for 105,4221 is 21105.
Thus, GCF of Fractions is 1/21105.Finally, GCF of Fractions for 6749/105, 4082/4221 is 1/21105.