GCF of 182/32, 434/670
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 182/32, 434/670 i.e 14/10720 easily. The following is the detailed procedure to determine the greatest common factor of fractions 182/32, 434/670.
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 182/32,434/670?
Given fractions are 182/32,434/670
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 182/32,434/670, numerators are 182,434
Denominators are 32,670
The GCF of 182,434 is 14 .
LCM of 32,670 is 10720.
The greatest common factor of 182/32,434/670 = [GCF of 182,434]/[LCM of 32,670]= 14/10720
Therefore, the GCF of 182/32,434/670 is 14/10720.
To find the highest common factor of 182,434, we have to find the factors of both numbers and list the highest common factor.
The factors of 182 are 1, 2, 7, 13, 14, 26, 91, 182
The factors of 434 are 1, 2, 7, 14, 31, 62, 217, 434
The HCF of 182,434 is 14.
Lets's calculate GCF of 182,434
| 2 | 182, 434 |
| 7 | 91, 217 |
| 13, 31 |
∴ So the GCF of the given numbers is 2 x 7 = 14
Greatest Common Factor of 182,434 By Matching Biggest Common Factor Method
Now, list down the factors of 182
:1,2,7,13,14,26,91,182
Now, list down the factors of 434
:1,2,7,14,31,62,217,434
Greatest Common Factor
We found the factors 182,434 . The biggest common factor number is the GCF number.
So the greatest common factor 182,434 is 14.
Lets's calculate LCM of 32,670
| 2 | 32, 670 |
| 16, 335 |
∴ So the LCM of the given numbers is 2 x 16 x 335 = 10720
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 14/10720
Therefore, the GCF of Fractions 182/32,434/670 is 14/10720
Least Common Multiple of 32,670 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 32,670 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(32,670) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(32,670) x common factors =2 x 1 = 2
LCM(32,670) = ( 32 × 670 ) / 2
LCM(32,670) = 21440 / 2
LCM(32,670) = 10720
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FAQs on GCF of Fractions of 182/32, 434/670
1. What is the HCF of 182,434?
The HCF of 182,434 is 14
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 182/32, 434/670?
Answer: GCF of Numerators as per given numbers 182/32, 434/670 is
GCF of Numerators i.e. for 182,434 is 14
LCM of denominators i.e. for 32,670 is 10720.
Thus, GCF of Fractions is 14/10720.Finally, GCF of Fractions for 182/32, 434/670 is 14/10720.