GCF of 66/599, 77/562, 749/742
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 66/599, 77/562, 749/742 i.e 1/124892698 easily. The following is the detailed procedure to determine the greatest common factor of fractions 66/599, 77/562, 749/742.
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 66/599,77/562,749/742?
Given fractions are 66/599,77/562,749/742
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 66/599,77/562,749/742, numerators are 66,77,749
Denominators are 599,562,742
The GCF of 66,77,749 is 1 .
LCM of 599,562,742 is 124892698.
The greatest common factor of 66/599,77/562,749/742 = [GCF of 66,77,749]/[LCM of 599,562,742]= 1/124892698
Therefore, the GCF of 66/599,77/562,749/742 is 1/124892698.
To find the highest common factor of 66,77,749, we have to find the factors of both numbers and list the highest common factor.
The factors of 66 are 1, 2, 3, 6, 11, 22, 33, 66
The factors of 77 are 1, 7, 11, 77
The factors of 749 are 1, 7, 107, 749
The HCF of 66,77,749 is 1.
Lets's calculate GCF of 66,77,749
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 66,77,749 By Matching Biggest Common Factor Method
Now, list down the factors of 66
:1,2,3,6,11,22,33,66
Now, list down the factors of 77
:1,7,11,77
Now, list down the factors of 749
:1,7,107,749
Greatest Common Factor
We found the factors 66,77,749 . The biggest common factor number is the GCF number.
So the greatest common factor 66,77,749 is 1.
Lets's calculate LCM of 599,562,742
| 2 | 599, 562, 742 |
| 599, 281, 371 |
∴ So the LCM of the given numbers is 2 x 599 x 281 x 371 = 124892698
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/124892698
Therefore, the GCF of Fractions 66/599,77/562,749/742 is 1/124892698
Least Common Multiple of 599,562,742 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 599,562,742 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(599,562,742) = 1
common factors(in case of two or more numbers have common factors) = 2
GCF(599,562,742) x common factors =1 x 2 = 2
LCM(599,562,742) = ( 599 × 562 × 742 ) / 2
LCM(599,562,742) = 249785396 / 2
LCM(599,562,742) = 124892698
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FAQs on GCF of Fractions of 66/599, 77/562, 749/742
1. What is the HCF of 66,77,749?
The HCF of 66,77,749 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 66/599, 77/562, 749/742?
Answer: GCF of Numerators as per given numbers 66/599, 77/562, 749/742 is
GCF of Numerators i.e. for 66,77,749 is 1
LCM of denominators i.e. for 599,562,742 is 124892698.
Thus, GCF of Fractions is 1/124892698.Finally, GCF of Fractions for 66/599, 77/562, 749/742 is 1/124892698.