GCF of 645/309, 752/234
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 645/309, 752/234 i.e 1/24102 easily. The following is the detailed procedure to determine the greatest common factor of fractions 645/309, 752/234.
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 645/309,752/234?
Given fractions are 645/309,752/234
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 645/309,752/234, numerators are 645,752
Denominators are 309,234
The GCF of 645,752 is 1 .
LCM of 309,234 is 24102.
The greatest common factor of 645/309,752/234 = [GCF of 645,752]/[LCM of 309,234]= 1/24102
Therefore, the GCF of 645/309,752/234 is 1/24102.
To find the highest common factor of 645,752, we have to find the factors of both numbers and list the highest common factor.
The factors of 645 are 1, 3, 5, 15, 43, 129, 215, 645
The factors of 752 are 1, 2, 4, 8, 16, 47, 94, 188, 376, 752
The HCF of 645,752 is 1.
Lets's calculate GCF of 645,752
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 645,752 By Matching Biggest Common Factor Method
Now, list down the factors of 645
:1,3,5,15,43,129,215,645
Now, list down the factors of 752
:1,2,4,8,16,47,94,188,376,752
Greatest Common Factor
We found the factors 645,752 . The biggest common factor number is the GCF number.
So the greatest common factor 645,752 is 1.
Lets's calculate LCM of 309,234
| 3 | 309, 234 |
| 103, 78 |
∴ So the LCM of the given numbers is 3 x 103 x 78 = 24102
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/24102
Therefore, the GCF of Fractions 645/309,752/234 is 1/24102
Least Common Multiple of 309,234 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 309,234 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(309,234) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(309,234) x common factors =3 x 1 = 3
LCM(309,234) = ( 309 × 234 ) / 3
LCM(309,234) = 72306 / 3
LCM(309,234) = 24102
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FAQs on GCF of Fractions of 645/309, 752/234
1. What is the HCF of 645,752?
The HCF of 645,752 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 645/309, 752/234?
Answer: GCF of Numerators as per given numbers 645/309, 752/234 is
GCF of Numerators i.e. for 645,752 is 1
LCM of denominators i.e. for 309,234 is 24102.
Thus, GCF of Fractions is 1/24102.Finally, GCF of Fractions for 645/309, 752/234 is 1/24102.