GCF of 592/516, 1582/214
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 592/516, 1582/214 i.e 2/55212 easily. The following is the detailed procedure to determine the greatest common factor of fractions 592/516, 1582/214.
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 592/516,1582/214?
Given fractions are 592/516,1582/214
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 592/516,1582/214, numerators are 592,1582
Denominators are 516,214
The GCF of 592,1582 is 2 .
LCM of 516,214 is 55212.
The greatest common factor of 592/516,1582/214 = [GCF of 592,1582]/[LCM of 516,214]= 2/55212
Therefore, the GCF of 592/516,1582/214 is 2/55212.
To find the highest common factor of 592,1582, we have to find the factors of both numbers and list the highest common factor.
The factors of 592 are 1, 2, 4, 8, 16, 37, 74, 148, 296, 592
The factors of 1582 are 1, 2, 7, 14, 113, 226, 791, 1582
The HCF of 592,1582 is 2.
Lets's calculate GCF of 592,1582
| 2 | 592, 1582 |
| 296, 791 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 592,1582 By Matching Biggest Common Factor Method
Now, list down the factors of 592
:1,2,4,8,16,37,74,148,296,592
Now, list down the factors of 1582
:1,2,7,14,113,226,791,1582
Greatest Common Factor
We found the factors 592,1582 . The biggest common factor number is the GCF number.
So the greatest common factor 592,1582 is 2.
Lets's calculate LCM of 516,214
| 2 | 516, 214 |
| 258, 107 |
∴ So the LCM of the given numbers is 2 x 258 x 107 = 55212
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/55212
Therefore, the GCF of Fractions 592/516,1582/214 is 2/55212
Least Common Multiple of 516,214 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 516,214 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(516,214) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(516,214) x common factors =2 x 1 = 2
LCM(516,214) = ( 516 × 214 ) / 2
LCM(516,214) = 110424 / 2
LCM(516,214) = 55212
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FAQs on GCF of Fractions of 592/516, 1582/214
1. What is the HCF of 592,1582?
The HCF of 592,1582 is 2
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 592/516, 1582/214?
Answer: GCF of Numerators as per given numbers 592/516, 1582/214 is
GCF of Numerators i.e. for 592,1582 is 2
LCM of denominators i.e. for 516,214 is 55212.
Thus, GCF of Fractions is 2/55212.Finally, GCF of Fractions for 592/516, 1582/214 is 2/55212.