GCF of 462/33, 172/145
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 462/33, 172/145 i.e 2/4785 easily. The following is the detailed procedure to determine the greatest common factor of fractions 462/33, 172/145.
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 462/33,172/145?
Given fractions are 462/33,172/145
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 462/33,172/145, numerators are 462,172
Denominators are 33,145
The GCF of 462,172 is 2 .
LCM of 33,145 is 4785.
The greatest common factor of 462/33,172/145 = [GCF of 462,172]/[LCM of 33,145]= 2/4785
Therefore, the GCF of 462/33,172/145 is 2/4785.
To find the highest common factor of 462,172, we have to find the factors of both numbers and list the highest common factor.
The factors of 462 are 1, 2, 3, 6, 7, 11, 14, 21, 22, 33, 42, 66, 77, 154, 231, 462
The factors of 172 are 1, 2, 4, 43, 86, 172
The HCF of 462,172 is 2.
Lets's calculate GCF of 462,172
| 2 | 462, 172 |
| 231, 86 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 462,172 By Matching Biggest Common Factor Method
Now, list down the factors of 462
:1,2,3,6,7,11,14,21,22,33,42,66,77,154,231,462
Now, list down the factors of 172
:1,2,4,43,86,172
Greatest Common Factor
We found the factors 462,172 . The biggest common factor number is the GCF number.
So the greatest common factor 462,172 is 2.
Lets's calculate LCM of 33,145
Given numbers has no common factors except 1. So, there LCM is their product i.e 4785
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/4785
Therefore, the GCF of Fractions 462/33,172/145 is 2/4785
Least Common Multiple of 33,145 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 33,145 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(33,145) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(33,145) x common factors =1 x 1 = 1
LCM(33,145) = ( 33 × 145 ) / 1
LCM(33,145) = 4785 / 1
LCM(33,145) = 4785
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FAQs on GCF of Fractions of 462/33, 172/145
1. What is the HCF of 462,172?
The HCF of 462,172 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 462/33, 172/145?
Answer: GCF of Numerators as per given numbers 462/33, 172/145 is
GCF of Numerators i.e. for 462,172 is 2
LCM of denominators i.e. for 33,145 is 4785.
Thus, GCF of Fractions is 2/4785.Finally, GCF of Fractions for 462/33, 172/145 is 2/4785.