GCF of 582/630, 281/420
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 582/630, 281/420 i.e 1/1260 easily. The following is the detailed procedure to determine the greatest common factor of fractions 582/630, 281/420.
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 582/630,281/420?
Given fractions are 582/630,281/420
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 582/630,281/420, numerators are 582,281
Denominators are 630,420
The GCF of 582,281 is 1 .
LCM of 630,420 is 1260.
The greatest common factor of 582/630,281/420 = [GCF of 582,281]/[LCM of 630,420]= 1/1260
Therefore, the GCF of 582/630,281/420 is 1/1260.
To find the highest common factor of 582,281, we have to find the factors of both numbers and list the highest common factor.
The factors of 582 are 1, 2, 3, 6, 97, 194, 291, 582
The factors of 281 are 1, 281
The HCF of 582,281 is 1.
Lets's calculate GCF of 582,281
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 582,281 By Matching Biggest Common Factor Method
Now, list down the factors of 582
:1,2,3,6,97,194,291,582
Now, list down the factors of 281
:1,281
Greatest Common Factor
We found the factors 582,281 . The biggest common factor number is the GCF number.
So the greatest common factor 582,281 is 1.
Lets's calculate LCM of 630,420
| 2 | 630, 420 |
| 3 | 315, 210 |
| 5 | 105, 70 |
| 7 | 21, 14 |
| 3, 2 |
∴ So the LCM of the given numbers is 2 x 3 x 5 x 7 x 3 x 2 = 1260
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/1260
Therefore, the GCF of Fractions 582/630,281/420 is 1/1260
Least Common Multiple of 630,420 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 630,420 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(630,420) = 210
common factors(in case of two or more numbers have common factors) = 1
GCF(630,420) x common factors =210 x 1 = 210
LCM(630,420) = ( 630 × 420 ) / 210
LCM(630,420) = 264600 / 210
LCM(630,420) = 1260
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FAQs on GCF of Fractions of 582/630, 281/420
1. What is the HCF of 582,281?
The HCF of 582,281 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 582/630, 281/420?
Answer: GCF of Numerators as per given numbers 582/630, 281/420 is
GCF of Numerators i.e. for 582,281 is 1
LCM of denominators i.e. for 630,420 is 1260.
Thus, GCF of Fractions is 1/1260.Finally, GCF of Fractions for 582/630, 281/420 is 1/1260.