GCF of 570/217, 532/219
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 570/217, 532/219 i.e 38/47523 easily. The following is the detailed procedure to determine the greatest common factor of fractions 570/217, 532/219.
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 570/217,532/219?
Given fractions are 570/217,532/219
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 570/217,532/219, numerators are 570,532
Denominators are 217,219
The GCF of 570,532 is 38 .
LCM of 217,219 is 47523.
The greatest common factor of 570/217,532/219 = [GCF of 570,532]/[LCM of 217,219]= 38/47523
Therefore, the GCF of 570/217,532/219 is 38/47523.
To find the highest common factor of 570,532, we have to find the factors of both numbers and list the highest common factor.
The factors of 570 are 1, 2, 3, 5, 6, 10, 15, 19, 30, 38, 57, 95, 114, 190, 285, 570
The factors of 532 are 1, 2, 4, 7, 14, 19, 28, 38, 76, 133, 266, 532
The HCF of 570,532 is 38.
Lets's calculate GCF of 570,532
| 2 | 570, 532 |
| 19 | 285, 266 |
| 15, 14 |
∴ So the GCF of the given numbers is 2 x 19 = 38
Greatest Common Factor of 570,532 By Matching Biggest Common Factor Method
Now, list down the factors of 570
:1,2,3,5,6,10,15,19,30,38,57,95,114,190,285,570
Now, list down the factors of 532
:1,2,4,7,14,19,28,38,76,133,266,532
Greatest Common Factor
We found the factors 570,532 . The biggest common factor number is the GCF number.
So the greatest common factor 570,532 is 38.
Lets's calculate LCM of 217,219
Given numbers has no common factors except 1. So, there LCM is their product i.e 47523
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 38/47523
Therefore, the GCF of Fractions 570/217,532/219 is 38/47523
Least Common Multiple of 217,219 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 217,219 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(217,219) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(217,219) x common factors =1 x 1 = 1
LCM(217,219) = ( 217 × 219 ) / 1
LCM(217,219) = 47523 / 1
LCM(217,219) = 47523
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FAQs on GCF of Fractions of 570/217, 532/219
1. What is the HCF of 570,532?
The HCF of 570,532 is 38
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 570/217, 532/219?
Answer: GCF of Numerators as per given numbers 570/217, 532/219 is
GCF of Numerators i.e. for 570,532 is 38
LCM of denominators i.e. for 217,219 is 47523.
Thus, GCF of Fractions is 38/47523.Finally, GCF of Fractions for 570/217, 532/219 is 38/47523.