GCF of 804/172, 1656/176
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 804/172, 1656/176 i.e 12/7568 easily. The following is the detailed procedure to determine the greatest common factor of fractions 804/172, 1656/176.
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 804/172,1656/176?
Given fractions are 804/172,1656/176
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 804/172,1656/176, numerators are 804,1656
Denominators are 172,176
The GCF of 804,1656 is 12 .
LCM of 172,176 is 7568.
The greatest common factor of 804/172,1656/176 = [GCF of 804,1656]/[LCM of 172,176]= 12/7568
Therefore, the GCF of 804/172,1656/176 is 12/7568.
To find the highest common factor of 804,1656, we have to find the factors of both numbers and list the highest common factor.
The factors of 804 are 1, 2, 3, 4, 6, 12, 67, 134, 201, 268, 402, 804
The factors of 1656 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 23, 24, 36, 46, 69, 72, 92, 138, 184, 207, 276, 414, 552, 828, 1656
The HCF of 804,1656 is 12.
Lets's calculate GCF of 804,1656
| 2 | 804, 1656 |
| 2 | 402, 828 |
| 3 | 201, 414 |
| 67, 138 |
∴ So the GCF of the given numbers is 2 x 2 x 3 = 12
Greatest Common Factor of 804,1656 By Matching Biggest Common Factor Method
Now, list down the factors of 804
:1,2,3,4,6,12,67,134,201,268,402,804
Now, list down the factors of 1656
:1,2,3,4,6,8,9,12,18,23,24,36,46,69,72,92,138,184,207,276,414,552,828,1656
Greatest Common Factor
We found the factors 804,1656 . The biggest common factor number is the GCF number.
So the greatest common factor 804,1656 is 12.
Lets's calculate LCM of 172,176
| 2 | 172, 176 |
| 2 | 86, 88 |
| 43, 44 |
∴ So the LCM of the given numbers is 2 x 2 x 43 x 44 = 7568
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 12/7568
Therefore, the GCF of Fractions 804/172,1656/176 is 12/7568
Least Common Multiple of 172,176 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 172,176 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(172,176) = 4
common factors(in case of two or more numbers have common factors) = 1
GCF(172,176) x common factors =4 x 1 = 4
LCM(172,176) = ( 172 × 176 ) / 4
LCM(172,176) = 30272 / 4
LCM(172,176) = 7568
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FAQs on GCF of Fractions of 804/172, 1656/176
1. What is the HCF of 804,1656?
The HCF of 804,1656 is 12
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 804/172, 1656/176?
Answer: GCF of Numerators as per given numbers 804/172, 1656/176 is
GCF of Numerators i.e. for 804,1656 is 12
LCM of denominators i.e. for 172,176 is 7568.
Thus, GCF of Fractions is 12/7568.Finally, GCF of Fractions for 804/172, 1656/176 is 12/7568.