GCF of 168/302, 140/446
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 168/302, 140/446 i.e 28/67346 easily. The following is the detailed procedure to determine the greatest common factor of fractions 168/302, 140/446.
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 168/302,140/446?
Given fractions are 168/302,140/446
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 168/302,140/446, numerators are 168,140
Denominators are 302,446
The GCF of 168,140 is 28 .
LCM of 302,446 is 67346.
The greatest common factor of 168/302,140/446 = [GCF of 168,140]/[LCM of 302,446]= 28/67346
Therefore, the GCF of 168/302,140/446 is 28/67346.
To find the highest common factor of 168,140, 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 140 are 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70, 140
The HCF of 168,140 is 28.
Lets's calculate GCF of 168,140
| 2 | 168, 140 |
| 2 | 84, 70 |
| 7 | 42, 35 |
| 6, 5 |
∴ So the GCF of the given numbers is 2 x 2 x 7 = 28
Greatest Common Factor of 168,140 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 140
:1,2,4,5,7,10,14,20,28,35,70,140
Greatest Common Factor
We found the factors 168,140 . The biggest common factor number is the GCF number.
So the greatest common factor 168,140 is 28.
Lets's calculate LCM of 302,446
| 2 | 302, 446 |
| 151, 223 |
∴ So the LCM of the given numbers is 2 x 151 x 223 = 67346
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 28/67346
Therefore, the GCF of Fractions 168/302,140/446 is 28/67346
Least Common Multiple of 302,446 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 302,446 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(302,446) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(302,446) x common factors =2 x 1 = 2
LCM(302,446) = ( 302 × 446 ) / 2
LCM(302,446) = 134692 / 2
LCM(302,446) = 67346
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FAQs on GCF of Fractions of 168/302, 140/446
1. What is the HCF of 168,140?
The HCF of 168,140 is 28
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 168/302, 140/446?
Answer: GCF of Numerators as per given numbers 168/302, 140/446 is
GCF of Numerators i.e. for 168,140 is 28
LCM of denominators i.e. for 302,446 is 67346.
Thus, GCF of Fractions is 28/67346.Finally, GCF of Fractions for 168/302, 140/446 is 28/67346.