GCF of 13/17, 66/51, 49/56, 34/21
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 13/17, 66/51, 49/56, 34/21 i.e 1/2856 easily. The following is the detailed procedure to determine the greatest common factor of fractions 13/17, 66/51, 49/56, 34/21.
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 13/17,66/51,49/56,34/21?
Given fractions are 13/17,66/51,49/56,34/21
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 13/17,66/51,49/56,34/21, numerators are 13,66,49,34
Denominators are 17,51,56,21
The GCF of 13,66,49,34 is 1 .
LCM of 17,51,56,21 is 2856.
The greatest common factor of 13/17,66/51,49/56,34/21 = [GCF of 13,66,49,34]/[LCM of 17,51,56,21]= 1/2856
Therefore, the GCF of 13/17,66/51,49/56,34/21 is 1/2856.
To find the highest common factor of 13,66,49,34, we have to find the factors of both numbers and list the highest common factor.
The factors of 13 are 1, 13
The factors of 66 are 1, 2, 3, 6, 11, 22, 33, 66
The factors of 49 are 1, 7, 49
The factors of 34 are 1, 2, 17, 34
The HCF of 13,66,49,34 is 1.
Lets's calculate GCF of 13,66,49,34
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 13,66,49,34 By Matching Biggest Common Factor Method
Now, list down the factors of 13
:1,13
Now, list down the factors of 66
:1,2,3,6,11,22,33,66
Now, list down the factors of 49
:1,7,49
Now, list down the factors of 34
:1,2,17,34
Greatest Common Factor
We found the factors 13,66,49,34 . The biggest common factor number is the GCF number.
So the greatest common factor 13,66,49,34 is 1.
Lets's calculate LCM of 17,51,56,21
| 3 | 17, 51, 56, 21 |
| 7 | 17, 17, 56, 7 |
| 17 | 17, 17, 8, 1 |
| 1, 1, 8, 1 |
∴ So the LCM of the given numbers is 3 x 7 x 17 x 1 x 1 x 8 x 1 = 2856
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/2856
Therefore, the GCF of Fractions 13/17,66/51,49/56,34/21 is 1/2856
Least Common Multiple of 17,51,56,21 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 17,51,56,21 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(17,51,56,21) = 1
common factors(in case of two or more numbers have common factors) = 357
GCF(17,51,56,21) x common factors =1 x 357 = 357
LCM(17,51,56,21) = ( 17 × 51 × 56 × 21 ) / 357
LCM(17,51,56,21) = 1019592 / 357
LCM(17,51,56,21) = 2856
GCF of Fractions Calculation Examples
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FAQs on GCF of Fractions of 13/17, 66/51, 49/56, 34/21
1. What is the HCF of 13,66,49,34?
The HCF of 13,66,49,34 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 13/17, 66/51, 49/56, 34/21?
Answer: GCF of Numerators as per given numbers 13/17, 66/51, 49/56, 34/21 is
GCF of Numerators i.e. for 13,66,49,34 is 1
LCM of denominators i.e. for 17,51,56,21 is 2856.
Thus, GCF of Fractions is 1/2856.Finally, GCF of Fractions for 13/17, 66/51, 49/56, 34/21 is 1/2856.