GCF of 3658/724, 9765/377
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 3658/724, 9765/377 i.e 31/272948 easily. The following is the detailed procedure to determine the greatest common factor of fractions 3658/724, 9765/377.
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 3658/724,9765/377?
Given fractions are 3658/724,9765/377
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 3658/724,9765/377, numerators are 3658,9765
Denominators are 724,377
The GCF of 3658,9765 is 31 .
LCM of 724,377 is 272948.
The greatest common factor of 3658/724,9765/377 = [GCF of 3658,9765]/[LCM of 724,377]= 31/272948
Therefore, the GCF of 3658/724,9765/377 is 31/272948.
To find the highest common factor of 3658,9765, we have to find the factors of both numbers and list the highest common factor.
The factors of 3658 are 1, 2, 31, 59, 62, 118, 1829, 3658
The factors of 9765 are 1, 3, 5, 7, 9, 15, 21, 31, 35, 45, 63, 93, 105, 155, 217, 279, 315, 465, 651, 1085, 1395, 1953, 3255, 9765
The HCF of 3658,9765 is 31.
Lets's calculate GCF of 3658,9765
| 31 | 3658, 9765 |
| 118, 315 |
∴ So the GCF of the given numbers is 31 = 31
Greatest Common Factor of 3658,9765 By Matching Biggest Common Factor Method
Now, list down the factors of 3658
:1,2,31,59,62,118,1829,3658
Now, list down the factors of 9765
:1,3,5,7,9,15,21,31,35,45,63,93,105,155,217,279,315,465,651,1085,1395,1953,3255,9765
Greatest Common Factor
We found the factors 3658,9765 . The biggest common factor number is the GCF number.
So the greatest common factor 3658,9765 is 31.
Lets's calculate LCM of 724,377
Given numbers has no common factors except 1. So, there LCM is their product i.e 272948
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 31/272948
Therefore, the GCF of Fractions 3658/724,9765/377 is 31/272948
Least Common Multiple of 724,377 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 724,377 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(724,377) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(724,377) x common factors =1 x 1 = 1
LCM(724,377) = ( 724 × 377 ) / 1
LCM(724,377) = 272948 / 1
LCM(724,377) = 272948
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FAQs on GCF of Fractions of 3658/724, 9765/377
1. What is the HCF of 3658,9765?
The HCF of 3658,9765 is 31
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 3658/724, 9765/377?
Answer: GCF of Numerators as per given numbers 3658/724, 9765/377 is
GCF of Numerators i.e. for 3658,9765 is 31
LCM of denominators i.e. for 724,377 is 272948.
Thus, GCF of Fractions is 31/272948.Finally, GCF of Fractions for 3658/724, 9765/377 is 31/272948.