GCF of 34/245, 42/182, 470/445
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 34/245, 42/182, 470/445 i.e 2/566930 easily. The following is the detailed procedure to determine the greatest common factor of fractions 34/245, 42/182, 470/445.
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 34/245,42/182,470/445?
Given fractions are 34/245,42/182,470/445
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 34/245,42/182,470/445, numerators are 34,42,470
Denominators are 245,182,445
The GCF of 34,42,470 is 2 .
LCM of 245,182,445 is 566930.
The greatest common factor of 34/245,42/182,470/445 = [GCF of 34,42,470]/[LCM of 245,182,445]= 2/566930
Therefore, the GCF of 34/245,42/182,470/445 is 2/566930.
To find the highest common factor of 34,42,470, we have to find the factors of both numbers and list the highest common factor.
The factors of 34 are 1, 2, 17, 34
The factors of 42 are 1, 2, 3, 6, 7, 14, 21, 42
The factors of 470 are 1, 2, 5, 10, 47, 94, 235, 470
The HCF of 34,42,470 is 2.
Lets's calculate GCF of 34,42,470
| 2 | 34, 42, 470 |
| 17, 21, 235 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 34,42,470 By Matching Biggest Common Factor Method
Now, list down the factors of 34
:1,2,17,34
Now, list down the factors of 42
:1,2,3,6,7,14,21,42
Now, list down the factors of 470
:1,2,5,10,47,94,235,470
Greatest Common Factor
We found the factors 34,42,470 . The biggest common factor number is the GCF number.
So the greatest common factor 34,42,470 is 2.
Lets's calculate LCM of 245,182,445
| 5 | 245, 182, 445 |
| 7 | 49, 182, 89 |
| 7, 26, 89 |
∴ So the LCM of the given numbers is 5 x 7 x 7 x 26 x 89 = 566930
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/566930
Therefore, the GCF of Fractions 34/245,42/182,470/445 is 2/566930
Least Common Multiple of 245,182,445 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 245,182,445 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(245,182,445) = 1
common factors(in case of two or more numbers have common factors) = 35
GCF(245,182,445) x common factors =1 x 35 = 35
LCM(245,182,445) = ( 245 × 182 × 445 ) / 35
LCM(245,182,445) = 19842550 / 35
LCM(245,182,445) = 566930
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FAQs on GCF of Fractions of 34/245, 42/182, 470/445
1. What is the HCF of 34,42,470?
The HCF of 34,42,470 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 34/245, 42/182, 470/445?
Answer: GCF of Numerators as per given numbers 34/245, 42/182, 470/445 is
GCF of Numerators i.e. for 34,42,470 is 2
LCM of denominators i.e. for 245,182,445 is 566930.
Thus, GCF of Fractions is 2/566930.Finally, GCF of Fractions for 34/245, 42/182, 470/445 is 2/566930.