GCF of 374/345, 408/582
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 374/345, 408/582 i.e 34/66930 easily. The following is the detailed procedure to determine the greatest common factor of fractions 374/345, 408/582.
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 374/345,408/582?
Given fractions are 374/345,408/582
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 374/345,408/582, numerators are 374,408
Denominators are 345,582
The GCF of 374,408 is 34 .
LCM of 345,582 is 66930.
The greatest common factor of 374/345,408/582 = [GCF of 374,408]/[LCM of 345,582]= 34/66930
Therefore, the GCF of 374/345,408/582 is 34/66930.
To find the highest common factor of 374,408, we have to find the factors of both numbers and list the highest common factor.
The factors of 374 are 1, 2, 11, 17, 22, 34, 187, 374
The factors of 408 are 1, 2, 3, 4, 6, 8, 12, 17, 24, 34, 51, 68, 102, 136, 204, 408
The HCF of 374,408 is 34.
Lets's calculate GCF of 374,408
| 2 | 374, 408 |
| 17 | 187, 204 |
| 11, 12 |
∴ So the GCF of the given numbers is 2 x 17 = 34
Greatest Common Factor of 374,408 By Matching Biggest Common Factor Method
Now, list down the factors of 374
:1,2,11,17,22,34,187,374
Now, list down the factors of 408
:1,2,3,4,6,8,12,17,24,34,51,68,102,136,204,408
Greatest Common Factor
We found the factors 374,408 . The biggest common factor number is the GCF number.
So the greatest common factor 374,408 is 34.
Lets's calculate LCM of 345,582
| 3 | 345, 582 |
| 115, 194 |
∴ So the LCM of the given numbers is 3 x 115 x 194 = 66930
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 34/66930
Therefore, the GCF of Fractions 374/345,408/582 is 34/66930
Least Common Multiple of 345,582 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 345,582 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(345,582) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(345,582) x common factors =3 x 1 = 3
LCM(345,582) = ( 345 × 582 ) / 3
LCM(345,582) = 200790 / 3
LCM(345,582) = 66930
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FAQs on GCF of Fractions of 374/345, 408/582
1. What is the HCF of 374,408?
The HCF of 374,408 is 34
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 374/345, 408/582?
Answer: GCF of Numerators as per given numbers 374/345, 408/582 is
GCF of Numerators i.e. for 374,408 is 34
LCM of denominators i.e. for 345,582 is 66930.
Thus, GCF of Fractions is 34/66930.Finally, GCF of Fractions for 374/345, 408/582 is 34/66930.