GCF of 1296/178, 8172/6442
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1296/178, 8172/6442 i.e 36/573338 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1296/178, 8172/6442.
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 1296/178,8172/6442?
Given fractions are 1296/178,8172/6442
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 1296/178,8172/6442, numerators are 1296,8172
Denominators are 178,6442
The GCF of 1296,8172 is 36 .
LCM of 178,6442 is 573338.
The greatest common factor of 1296/178,8172/6442 = [GCF of 1296,8172]/[LCM of 178,6442]= 36/573338
Therefore, the GCF of 1296/178,8172/6442 is 36/573338.
To find the highest common factor of 1296,8172, we have to find the factors of both numbers and list the highest common factor.
The factors of 1296 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 36, 48, 54, 72, 81, 108, 144, 162, 216, 324, 432, 648, 1296
The factors of 8172 are 1, 2, 3, 4, 6, 9, 12, 18, 36, 227, 454, 681, 908, 1362, 2043, 2724, 4086, 8172
The HCF of 1296,8172 is 36.
Lets's calculate GCF of 1296,8172
| 2 | 1296, 8172 |
| 2 | 648, 4086 |
| 3 | 324, 2043 |
| 3 | 108, 681 |
| 36, 227 |
∴ So the GCF of the given numbers is 2 x 2 x 3 x 3 = 36
Greatest Common Factor of 1296,8172 By Matching Biggest Common Factor Method
Now, list down the factors of 1296
:1,2,3,4,6,8,9,12,16,18,24,27,36,48,54,72,81,108,144,162,216,324,432,648,1296
Now, list down the factors of 8172
:1,2,3,4,6,9,12,18,36,227,454,681,908,1362,2043,2724,4086,8172
Greatest Common Factor
We found the factors 1296,8172 . The biggest common factor number is the GCF number.
So the greatest common factor 1296,8172 is 36.
Lets's calculate LCM of 178,6442
| 2 | 178, 6442 |
| 89, 3221 |
∴ So the LCM of the given numbers is 2 x 89 x 3221 = 573338
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 36/573338
Therefore, the GCF of Fractions 1296/178,8172/6442 is 36/573338
Least Common Multiple of 178,6442 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 178,6442 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(178,6442) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(178,6442) x common factors =2 x 1 = 2
LCM(178,6442) = ( 178 × 6442 ) / 2
LCM(178,6442) = 1146676 / 2
LCM(178,6442) = 573338
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FAQs on GCF of Fractions of 1296/178, 8172/6442
1. What is the HCF of 1296,8172?
The HCF of 1296,8172 is 36
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 1296/178, 8172/6442?
Answer: GCF of Numerators as per given numbers 1296/178, 8172/6442 is
GCF of Numerators i.e. for 1296,8172 is 36
LCM of denominators i.e. for 178,6442 is 573338.
Thus, GCF of Fractions is 36/573338.Finally, GCF of Fractions for 1296/178, 8172/6442 is 36/573338.