GCF of 8577/282, 5628/406
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 8577/282, 5628/406 i.e 3/57246 easily. The following is the detailed procedure to determine the greatest common factor of fractions 8577/282, 5628/406.
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 8577/282,5628/406?
Given fractions are 8577/282,5628/406
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 8577/282,5628/406, numerators are 8577,5628
Denominators are 282,406
The GCF of 8577,5628 is 3 .
LCM of 282,406 is 57246.
The greatest common factor of 8577/282,5628/406 = [GCF of 8577,5628]/[LCM of 282,406]= 3/57246
Therefore, the GCF of 8577/282,5628/406 is 3/57246.
To find the highest common factor of 8577,5628, we have to find the factors of both numbers and list the highest common factor.
The factors of 8577 are 1, 3, 9, 953, 2859, 8577
The factors of 5628 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 67, 84, 134, 201, 268, 402, 469, 804, 938, 1407, 1876, 2814, 5628
The HCF of 8577,5628 is 3.
Lets's calculate GCF of 8577,5628
| 3 | 8577, 5628 |
| 2859, 1876 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 8577,5628 By Matching Biggest Common Factor Method
Now, list down the factors of 8577
:1,3,9,953,2859,8577
Now, list down the factors of 5628
:1,2,3,4,6,7,12,14,21,28,42,67,84,134,201,268,402,469,804,938,1407,1876,2814,5628
Greatest Common Factor
We found the factors 8577,5628 . The biggest common factor number is the GCF number.
So the greatest common factor 8577,5628 is 3.
Lets's calculate LCM of 282,406
| 2 | 282, 406 |
| 141, 203 |
∴ So the LCM of the given numbers is 2 x 141 x 203 = 57246
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/57246
Therefore, the GCF of Fractions 8577/282,5628/406 is 3/57246
Least Common Multiple of 282,406 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 282,406 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(282,406) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(282,406) x common factors =2 x 1 = 2
LCM(282,406) = ( 282 × 406 ) / 2
LCM(282,406) = 114492 / 2
LCM(282,406) = 57246
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FAQs on GCF of Fractions of 8577/282, 5628/406
1. What is the HCF of 8577,5628?
The HCF of 8577,5628 is 3
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 8577/282, 5628/406?
Answer: GCF of Numerators as per given numbers 8577/282, 5628/406 is
GCF of Numerators i.e. for 8577,5628 is 3
LCM of denominators i.e. for 282,406 is 57246.
Thus, GCF of Fractions is 3/57246.Finally, GCF of Fractions for 8577/282, 5628/406 is 3/57246.