GCF of 251/29, 748/69, 678/31
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 251/29, 748/69, 678/31 i.e 1/62031 easily. The following is the detailed procedure to determine the greatest common factor of fractions 251/29, 748/69, 678/31.
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 251/29,748/69,678/31?
Given fractions are 251/29,748/69,678/31
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 251/29,748/69,678/31, numerators are 251,748,678
Denominators are 29,69,31
The GCF of 251,748,678 is 1 .
LCM of 29,69,31 is 62031.
The greatest common factor of 251/29,748/69,678/31 = [GCF of 251,748,678]/[LCM of 29,69,31]= 1/62031
Therefore, the GCF of 251/29,748/69,678/31 is 1/62031.
To find the highest common factor of 251,748,678, we have to find the factors of both numbers and list the highest common factor.
The factors of 251 are 1, 251
The factors of 748 are 1, 2, 4, 11, 17, 22, 34, 44, 68, 187, 374, 748
The factors of 678 are 1, 2, 3, 6, 113, 226, 339, 678
The HCF of 251,748,678 is 1.
Lets's calculate GCF of 251,748,678
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 251,748,678 By Matching Biggest Common Factor Method
Now, list down the factors of 251
:1,251
Now, list down the factors of 748
:1,2,4,11,17,22,34,44,68,187,374,748
Now, list down the factors of 678
:1,2,3,6,113,226,339,678
Greatest Common Factor
We found the factors 251,748,678 . The biggest common factor number is the GCF number.
So the greatest common factor 251,748,678 is 1.
Lets's calculate LCM of 29,69,31
Given numbers has no common factors except 1. So, there LCM is their product i.e 62031
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/62031
Therefore, the GCF of Fractions 251/29,748/69,678/31 is 1/62031
Least Common Multiple of 29,69,31 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 29,69,31 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(29,69,31) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(29,69,31) x common factors =1 x 1 = 1
LCM(29,69,31) = ( 29 × 69 × 31 ) / 1
LCM(29,69,31) = 62031 / 1
LCM(29,69,31) = 62031
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FAQs on GCF of Fractions of 251/29, 748/69, 678/31
1. What is the HCF of 251,748,678?
The HCF of 251,748,678 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 251/29, 748/69, 678/31?
Answer: GCF of Numerators as per given numbers 251/29, 748/69, 678/31 is
GCF of Numerators i.e. for 251,748,678 is 1
LCM of denominators i.e. for 29,69,31 is 62031.
Thus, GCF of Fractions is 1/62031.Finally, GCF of Fractions for 251/29, 748/69, 678/31 is 1/62031.