GCF of 162/77, 648/319
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 162/77, 648/319 i.e 162/2233 easily. The following is the detailed procedure to determine the greatest common factor of fractions 162/77, 648/319.
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 162/77,648/319?
Given fractions are 162/77,648/319
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 162/77,648/319, numerators are 162,648
Denominators are 77,319
The GCF of 162,648 is 162 .
LCM of 77,319 is 2233.
The greatest common factor of 162/77,648/319 = [GCF of 162,648]/[LCM of 77,319]= 162/2233
Therefore, the GCF of 162/77,648/319 is 162/2233.
To find the highest common factor of 162,648, we have to find the factors of both numbers and list the highest common factor.
The factors of 162 are 1, 2, 3, 6, 9, 18, 27, 54, 81, 162
The factors of 648 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 81, 108, 162, 216, 324, 648
The HCF of 162,648 is 162.
Lets's calculate GCF of 162,648
| 2 | 162, 648 |
| 3 | 81, 324 |
| 3 | 27, 108 |
| 3 | 9, 36 |
| 3 | 3, 12 |
| 1, 4 |
∴ So the GCF of the given numbers is 2 x 3 x 3 x 3 x 3 = 162
Greatest Common Factor of 162,648 By Matching Biggest Common Factor Method
Now, list down the factors of 162
:1,2,3,6,9,18,27,54,81,162
Now, list down the factors of 648
:1,2,3,4,6,8,9,12,18,24,27,36,54,72,81,108,162,216,324,648
Greatest Common Factor
We found the factors 162,648 . The biggest common factor number is the GCF number.
So the greatest common factor 162,648 is 162.
Lets's calculate LCM of 77,319
| 11 | 77, 319 |
| 7, 29 |
∴ So the LCM of the given numbers is 11 x 7 x 29 = 2233
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 162/2233
Therefore, the GCF of Fractions 162/77,648/319 is 162/2233
Least Common Multiple of 77,319 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 77,319 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(77,319) = 11
common factors(in case of two or more numbers have common factors) = 1
GCF(77,319) x common factors =11 x 1 = 11
LCM(77,319) = ( 77 × 319 ) / 11
LCM(77,319) = 24563 / 11
LCM(77,319) = 2233
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FAQs on GCF of Fractions of 162/77, 648/319
1. What is the HCF of 162,648?
The HCF of 162,648 is 162
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 162/77, 648/319?
Answer: GCF of Numerators as per given numbers 162/77, 648/319 is
GCF of Numerators i.e. for 162,648 is 162
LCM of denominators i.e. for 77,319 is 2233.
Thus, GCF of Fractions is 162/2233.Finally, GCF of Fractions for 162/77, 648/319 is 162/2233.