GCF of 458/620, 9702/832
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 458/620, 9702/832 i.e 2/128960 easily. The following is the detailed procedure to determine the greatest common factor of fractions 458/620, 9702/832.
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 458/620,9702/832?
Given fractions are 458/620,9702/832
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 458/620,9702/832, numerators are 458,9702
Denominators are 620,832
The GCF of 458,9702 is 2 .
LCM of 620,832 is 128960.
The greatest common factor of 458/620,9702/832 = [GCF of 458,9702]/[LCM of 620,832]= 2/128960
Therefore, the GCF of 458/620,9702/832 is 2/128960.
To find the highest common factor of 458,9702, we have to find the factors of both numbers and list the highest common factor.
The factors of 458 are 1, 2, 229, 458
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 HCF of 458,9702 is 2.
Lets's calculate GCF of 458,9702
| 2 | 458, 9702 |
| 229, 4851 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 458,9702 By Matching Biggest Common Factor Method
Now, list down the factors of 458
:1,2,229,458
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
Greatest Common Factor
We found the factors 458,9702 . The biggest common factor number is the GCF number.
So the greatest common factor 458,9702 is 2.
Lets's calculate LCM of 620,832
| 2 | 620, 832 |
| 2 | 310, 416 |
| 155, 208 |
∴ So the LCM of the given numbers is 2 x 2 x 155 x 208 = 128960
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/128960
Therefore, the GCF of Fractions 458/620,9702/832 is 2/128960
Least Common Multiple of 620,832 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 620,832 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(620,832) = 4
common factors(in case of two or more numbers have common factors) = 1
GCF(620,832) x common factors =4 x 1 = 4
LCM(620,832) = ( 620 × 832 ) / 4
LCM(620,832) = 515840 / 4
LCM(620,832) = 128960
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FAQs on GCF of Fractions of 458/620, 9702/832
1. What is the HCF of 458,9702?
The HCF of 458,9702 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 458/620, 9702/832?
Answer: GCF of Numerators as per given numbers 458/620, 9702/832 is
GCF of Numerators i.e. for 458,9702 is 2
LCM of denominators i.e. for 620,832 is 128960.
Thus, GCF of Fractions is 2/128960.Finally, GCF of Fractions for 458/620, 9702/832 is 2/128960.