GCF of 53/75, 282/37, 344/691
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 53/75, 282/37, 344/691 i.e 1/1917525 easily. The following is the detailed procedure to determine the greatest common factor of fractions 53/75, 282/37, 344/691.
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 53/75,282/37,344/691?
Given fractions are 53/75,282/37,344/691
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 53/75,282/37,344/691, numerators are 53,282,344
Denominators are 75,37,691
The GCF of 53,282,344 is 1 .
LCM of 75,37,691 is 1917525.
The greatest common factor of 53/75,282/37,344/691 = [GCF of 53,282,344]/[LCM of 75,37,691]= 1/1917525
Therefore, the GCF of 53/75,282/37,344/691 is 1/1917525.
To find the highest common factor of 53,282,344, we have to find the factors of both numbers and list the highest common factor.
The factors of 53 are 1, 53
The factors of 282 are 1, 2, 3, 6, 47, 94, 141, 282
The factors of 344 are 1, 2, 4, 8, 43, 86, 172, 344
The HCF of 53,282,344 is 1.
Lets's calculate GCF of 53,282,344
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 53,282,344 By Matching Biggest Common Factor Method
Now, list down the factors of 53
:1,53
Now, list down the factors of 282
:1,2,3,6,47,94,141,282
Now, list down the factors of 344
:1,2,4,8,43,86,172,344
Greatest Common Factor
We found the factors 53,282,344 . The biggest common factor number is the GCF number.
So the greatest common factor 53,282,344 is 1.
Lets's calculate LCM of 75,37,691
Given numbers has no common factors except 1. So, there LCM is their product i.e 1917525
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/1917525
Therefore, the GCF of Fractions 53/75,282/37,344/691 is 1/1917525
Least Common Multiple of 75,37,691 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 75,37,691 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(75,37,691) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(75,37,691) x common factors =1 x 1 = 1
LCM(75,37,691) = ( 75 × 37 × 691 ) / 1
LCM(75,37,691) = 1917525 / 1
LCM(75,37,691) = 1917525
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FAQs on GCF of Fractions of 53/75, 282/37, 344/691
1. What is the HCF of 53,282,344?
The HCF of 53,282,344 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 53/75, 282/37, 344/691?
Answer: GCF of Numerators as per given numbers 53/75, 282/37, 344/691 is
GCF of Numerators i.e. for 53,282,344 is 1
LCM of denominators i.e. for 75,37,691 is 1917525.
Thus, GCF of Fractions is 1/1917525.Finally, GCF of Fractions for 53/75, 282/37, 344/691 is 1/1917525.