GCF of 3213/870, 8568/234
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 3213/870, 8568/234 i.e 1071/33930 easily. The following is the detailed procedure to determine the greatest common factor of fractions 3213/870, 8568/234.
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 3213/870,8568/234?
Given fractions are 3213/870,8568/234
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 3213/870,8568/234, numerators are 3213,8568
Denominators are 870,234
The GCF of 3213,8568 is 1071 .
LCM of 870,234 is 33930.
The greatest common factor of 3213/870,8568/234 = [GCF of 3213,8568]/[LCM of 870,234]= 1071/33930
Therefore, the GCF of 3213/870,8568/234 is 1071/33930.
To find the highest common factor of 3213,8568, we have to find the factors of both numbers and list the highest common factor.
The factors of 3213 are 1, 3, 7, 9, 17, 21, 27, 51, 63, 119, 153, 189, 357, 459, 1071, 3213
The factors of 8568 are 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 17, 18, 21, 24, 28, 34, 36, 42, 51, 56, 63, 68, 72, 84, 102, 119, 126, 136, 153, 168, 204, 238, 252, 306, 357, 408, 476, 504, 612, 714, 952, 1071, 1224, 1428, 2142, 2856, 4284, 8568
The HCF of 3213,8568 is 1071.
Lets's calculate GCF of 3213,8568
| 3 | 3213, 8568 |
| 3 | 1071, 2856 |
| 7 | 357, 952 |
| 17 | 51, 136 |
| 3, 8 |
∴ So the GCF of the given numbers is 3 x 3 x 7 x 17 = 1071
Greatest Common Factor of 3213,8568 By Matching Biggest Common Factor Method
Now, list down the factors of 3213
:1,3,7,9,17,21,27,51,63,119,153,189,357,459,1071,3213
Now, list down the factors of 8568
:1,2,3,4,6,7,8,9,12,14,17,18,21,24,28,34,36,42,51,56,63,68,72,84,102,119,126,136,153,168,204,238,252,306,357,408,476,504,612,714,952,1071,1224,1428,2142,2856,4284,8568
Greatest Common Factor
We found the factors 3213,8568 . The biggest common factor number is the GCF number.
So the greatest common factor 3213,8568 is 1071.
Lets's calculate LCM of 870,234
| 2 | 870, 234 |
| 3 | 435, 117 |
| 145, 39 |
∴ So the LCM of the given numbers is 2 x 3 x 145 x 39 = 33930
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1071/33930
Therefore, the GCF of Fractions 3213/870,8568/234 is 1071/33930
Least Common Multiple of 870,234 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 870,234 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(870,234) = 6
common factors(in case of two or more numbers have common factors) = 1
GCF(870,234) x common factors =6 x 1 = 6
LCM(870,234) = ( 870 × 234 ) / 6
LCM(870,234) = 203580 / 6
LCM(870,234) = 33930
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FAQs on GCF of Fractions of 3213/870, 8568/234
1. What is the HCF of 3213,8568?
The HCF of 3213,8568 is 1071
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 3213/870, 8568/234?
Answer: GCF of Numerators as per given numbers 3213/870, 8568/234 is
GCF of Numerators i.e. for 3213,8568 is 1071
LCM of denominators i.e. for 870,234 is 33930.
Thus, GCF of Fractions is 1071/33930.Finally, GCF of Fractions for 3213/870, 8568/234 is 1071/33930.