GCF of 9702/270, 8464/162
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 9702/270, 8464/162 i.e 2/810 easily. The following is the detailed procedure to determine the greatest common factor of fractions 9702/270, 8464/162.
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 9702/270,8464/162?
Given fractions are 9702/270,8464/162
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 9702/270,8464/162, numerators are 9702,8464
Denominators are 270,162
The GCF of 9702,8464 is 2 .
LCM of 270,162 is 810.
The greatest common factor of 9702/270,8464/162 = [GCF of 9702,8464]/[LCM of 270,162]= 2/810
Therefore, the GCF of 9702/270,8464/162 is 2/810.
To find the highest common factor of 9702,8464, we have to find the factors of both numbers and list the highest common factor.
The factors of 9702 are 1, 2, 3, 6, 7, 9, 11, 14, 18, 21, 22, 33, 42, 49, 63, 66, 77, 98, 99, 126, 147, 154, 198, 231, 294, 441, 462, 539, 693, 882, 1078, 1386, 1617, 3234, 4851, 9702
The factors of 8464 are 1, 2, 4, 8, 16, 23, 46, 92, 184, 368, 529, 1058, 2116, 4232, 8464
The HCF of 9702,8464 is 2.
Lets's calculate GCF of 9702,8464
| 2 | 9702, 8464 |
| 4851, 4232 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 9702,8464 By Matching Biggest Common Factor Method
Now, list down the factors of 9702
:1,2,3,6,7,9,11,14,18,21,22,33,42,49,63,66,77,98,99,126,147,154,198,231,294,441,462,539,693,882,1078,1386,1617,3234,4851,9702
Now, list down the factors of 8464
:1,2,4,8,16,23,46,92,184,368,529,1058,2116,4232,8464
Greatest Common Factor
We found the factors 9702,8464 . The biggest common factor number is the GCF number.
So the greatest common factor 9702,8464 is 2.
Lets's calculate LCM of 270,162
| 2 | 270, 162 |
| 3 | 135, 81 |
| 3 | 45, 27 |
| 3 | 15, 9 |
| 5, 3 |
∴ So the LCM of the given numbers is 2 x 3 x 3 x 3 x 5 x 3 = 810
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/810
Therefore, the GCF of Fractions 9702/270,8464/162 is 2/810
Least Common Multiple of 270,162 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 270,162 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(270,162) = 54
common factors(in case of two or more numbers have common factors) = 1
GCF(270,162) x common factors =54 x 1 = 54
LCM(270,162) = ( 270 × 162 ) / 54
LCM(270,162) = 43740 / 54
LCM(270,162) = 810
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FAQs on GCF of Fractions of 9702/270, 8464/162
1. What is the HCF of 9702,8464?
The HCF of 9702,8464 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 9702/270, 8464/162?
Answer: GCF of Numerators as per given numbers 9702/270, 8464/162 is
GCF of Numerators i.e. for 9702,8464 is 2
LCM of denominators i.e. for 270,162 is 810.
Thus, GCF of Fractions is 2/810.Finally, GCF of Fractions for 9702/270, 8464/162 is 2/810.