GCF of 168/34, 322/5423
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 168/34, 322/5423 i.e 14/10846 easily. The following is the detailed procedure to determine the greatest common factor of fractions 168/34, 322/5423.
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 168/34,322/5423?
Given fractions are 168/34,322/5423
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 168/34,322/5423, numerators are 168,322
Denominators are 34,5423
The GCF of 168,322 is 14 .
LCM of 34,5423 is 10846.
The greatest common factor of 168/34,322/5423 = [GCF of 168,322]/[LCM of 34,5423]= 14/10846
Therefore, the GCF of 168/34,322/5423 is 14/10846.
To find the highest common factor of 168,322, we have to find the factors of both numbers and list the highest common factor.
The factors of 168 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, 168
The factors of 322 are 1, 2, 7, 14, 23, 46, 161, 322
The HCF of 168,322 is 14.
Lets's calculate GCF of 168,322
| 2 | 168, 322 |
| 7 | 84, 161 |
| 12, 23 |
∴ So the GCF of the given numbers is 2 x 7 = 14
Greatest Common Factor of 168,322 By Matching Biggest Common Factor Method
Now, list down the factors of 168
:1,2,3,4,6,7,8,12,14,21,24,28,42,56,84,168
Now, list down the factors of 322
:1,2,7,14,23,46,161,322
Greatest Common Factor
We found the factors 168,322 . The biggest common factor number is the GCF number.
So the greatest common factor 168,322 is 14.
Lets's calculate LCM of 34,5423
| 17 | 34, 5423 |
| 2, 319 |
∴ So the LCM of the given numbers is 17 x 2 x 319 = 10846
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 14/10846
Therefore, the GCF of Fractions 168/34,322/5423 is 14/10846
Least Common Multiple of 34,5423 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 34,5423 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(34,5423) = 17
common factors(in case of two or more numbers have common factors) = 1
GCF(34,5423) x common factors =17 x 1 = 17
LCM(34,5423) = ( 34 × 5423 ) / 17
LCM(34,5423) = 184382 / 17
LCM(34,5423) = 10846
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FAQs on GCF of Fractions of 168/34, 322/5423
1. What is the HCF of 168,322?
The HCF of 168,322 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 168/34, 322/5423?
Answer: GCF of Numerators as per given numbers 168/34, 322/5423 is
GCF of Numerators i.e. for 168,322 is 14
LCM of denominators i.e. for 34,5423 is 10846.
Thus, GCF of Fractions is 14/10846.Finally, GCF of Fractions for 168/34, 322/5423 is 14/10846.