GCF of 30/592, 31/749, 893/214
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 30/592, 31/749, 893/214 i.e 1/443408 easily. The following is the detailed procedure to determine the greatest common factor of fractions 30/592, 31/749, 893/214.
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 30/592,31/749,893/214?
Given fractions are 30/592,31/749,893/214
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 30/592,31/749,893/214, numerators are 30,31,893
Denominators are 592,749,214
The GCF of 30,31,893 is 1 .
LCM of 592,749,214 is 443408.
The greatest common factor of 30/592,31/749,893/214 = [GCF of 30,31,893]/[LCM of 592,749,214]= 1/443408
Therefore, the GCF of 30/592,31/749,893/214 is 1/443408.
To find the highest common factor of 30,31,893, we have to find the factors of both numbers and list the highest common factor.
The factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30
The factors of 31 are 1, 31
The factors of 893 are 1, 19, 47, 893
The HCF of 30,31,893 is 1.
Lets's calculate GCF of 30,31,893
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 30,31,893 By Matching Biggest Common Factor Method
Now, list down the factors of 30
:1,2,3,5,6,10,15,30
Now, list down the factors of 31
:1,31
Now, list down the factors of 893
:1,19,47,893
Greatest Common Factor
We found the factors 30,31,893 . The biggest common factor number is the GCF number.
So the greatest common factor 30,31,893 is 1.
Lets's calculate LCM of 592,749,214
| 2 | 592, 749, 214 |
| 107 | 296, 749, 107 |
| 296, 7, 1 |
∴ So the LCM of the given numbers is 2 x 107 x 296 x 7 x 1 = 443408
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/443408
Therefore, the GCF of Fractions 30/592,31/749,893/214 is 1/443408
Least Common Multiple of 592,749,214 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 592,749,214 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(592,749,214) = 1
common factors(in case of two or more numbers have common factors) = 214
GCF(592,749,214) x common factors =1 x 214 = 214
LCM(592,749,214) = ( 592 × 749 × 214 ) / 214
LCM(592,749,214) = 94889312 / 214
LCM(592,749,214) = 443408
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FAQs on GCF of Fractions of 30/592, 31/749, 893/214
1. What is the HCF of 30,31,893?
The HCF of 30,31,893 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 30/592, 31/749, 893/214?
Answer: GCF of Numerators as per given numbers 30/592, 31/749, 893/214 is
GCF of Numerators i.e. for 30,31,893 is 1
LCM of denominators i.e. for 592,749,214 is 443408.
Thus, GCF of Fractions is 1/443408.Finally, GCF of Fractions for 30/592, 31/749, 893/214 is 1/443408.