GCF of 3738/766, 3630/3646
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 3738/766, 3630/3646 i.e 6/1396418 easily. The following is the detailed procedure to determine the greatest common factor of fractions 3738/766, 3630/3646.
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 3738/766,3630/3646?
Given fractions are 3738/766,3630/3646
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 3738/766,3630/3646, numerators are 3738,3630
Denominators are 766,3646
The GCF of 3738,3630 is 6 .
LCM of 766,3646 is 1396418.
The greatest common factor of 3738/766,3630/3646 = [GCF of 3738,3630]/[LCM of 766,3646]= 6/1396418
Therefore, the GCF of 3738/766,3630/3646 is 6/1396418.
To find the highest common factor of 3738,3630, we have to find the factors of both numbers and list the highest common factor.
The factors of 3738 are 1, 2, 3, 6, 7, 14, 21, 42, 89, 178, 267, 534, 623, 1246, 1869, 3738
The factors of 3630 are 1, 2, 3, 5, 6, 10, 11, 15, 22, 30, 33, 55, 66, 110, 121, 165, 242, 330, 363, 605, 726, 1210, 1815, 3630
The HCF of 3738,3630 is 6.
Lets's calculate GCF of 3738,3630
| 2 | 3738, 3630 |
| 3 | 1869, 1815 |
| 623, 605 |
∴ So the GCF of the given numbers is 2 x 3 = 6
Greatest Common Factor of 3738,3630 By Matching Biggest Common Factor Method
Now, list down the factors of 3738
:1,2,3,6,7,14,21,42,89,178,267,534,623,1246,1869,3738
Now, list down the factors of 3630
:1,2,3,5,6,10,11,15,22,30,33,55,66,110,121,165,242,330,363,605,726,1210,1815,3630
Greatest Common Factor
We found the factors 3738,3630 . The biggest common factor number is the GCF number.
So the greatest common factor 3738,3630 is 6.
Lets's calculate LCM of 766,3646
| 2 | 766, 3646 |
| 383, 1823 |
∴ So the LCM of the given numbers is 2 x 383 x 1823 = 1396418
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/1396418
Therefore, the GCF of Fractions 3738/766,3630/3646 is 6/1396418
Least Common Multiple of 766,3646 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 766,3646 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(766,3646) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(766,3646) x common factors =2 x 1 = 2
LCM(766,3646) = ( 766 × 3646 ) / 2
LCM(766,3646) = 2792836 / 2
LCM(766,3646) = 1396418
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FAQs on GCF of Fractions of 3738/766, 3630/3646
1. What is the HCF of 3738,3630?
The HCF of 3738,3630 is 6
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 3738/766, 3630/3646?
Answer: GCF of Numerators as per given numbers 3738/766, 3630/3646 is
GCF of Numerators i.e. for 3738,3630 is 6
LCM of denominators i.e. for 766,3646 is 1396418.
Thus, GCF of Fractions is 6/1396418.Finally, GCF of Fractions for 3738/766, 3630/3646 is 6/1396418.