GCF of 462/302, 682/676
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 462/302, 682/676 i.e 22/102076 easily. The following is the detailed procedure to determine the greatest common factor of fractions 462/302, 682/676.
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 462/302,682/676?
Given fractions are 462/302,682/676
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 462/302,682/676, numerators are 462,682
Denominators are 302,676
The GCF of 462,682 is 22 .
LCM of 302,676 is 102076.
The greatest common factor of 462/302,682/676 = [GCF of 462,682]/[LCM of 302,676]= 22/102076
Therefore, the GCF of 462/302,682/676 is 22/102076.
To find the highest common factor of 462,682, we have to find the factors of both numbers and list the highest common factor.
The factors of 462 are 1, 2, 3, 6, 7, 11, 14, 21, 22, 33, 42, 66, 77, 154, 231, 462
The factors of 682 are 1, 2, 11, 22, 31, 62, 341, 682
The HCF of 462,682 is 22.
Lets's calculate GCF of 462,682
| 2 | 462, 682 |
| 11 | 231, 341 |
| 21, 31 |
∴ So the GCF of the given numbers is 2 x 11 = 22
Greatest Common Factor of 462,682 By Matching Biggest Common Factor Method
Now, list down the factors of 462
:1,2,3,6,7,11,14,21,22,33,42,66,77,154,231,462
Now, list down the factors of 682
:1,2,11,22,31,62,341,682
Greatest Common Factor
We found the factors 462,682 . The biggest common factor number is the GCF number.
So the greatest common factor 462,682 is 22.
Lets's calculate LCM of 302,676
| 2 | 302, 676 |
| 151, 338 |
∴ So the LCM of the given numbers is 2 x 151 x 338 = 102076
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 22/102076
Therefore, the GCF of Fractions 462/302,682/676 is 22/102076
Least Common Multiple of 302,676 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 302,676 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(302,676) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(302,676) x common factors =2 x 1 = 2
LCM(302,676) = ( 302 × 676 ) / 2
LCM(302,676) = 204152 / 2
LCM(302,676) = 102076
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FAQs on GCF of Fractions of 462/302, 682/676
1. What is the HCF of 462,682?
The HCF of 462,682 is 22
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 462/302, 682/676?
Answer: GCF of Numerators as per given numbers 462/302, 682/676 is
GCF of Numerators i.e. for 462,682 is 22
LCM of denominators i.e. for 302,676 is 102076.
Thus, GCF of Fractions is 22/102076.Finally, GCF of Fractions for 462/302, 682/676 is 22/102076.