GCF of 1232/312, 1408/8166
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1232/312, 1408/8166 i.e 176/424632 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1232/312, 1408/8166.
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 1232/312,1408/8166?
Given fractions are 1232/312,1408/8166
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 1232/312,1408/8166, numerators are 1232,1408
Denominators are 312,8166
The GCF of 1232,1408 is 176 .
LCM of 312,8166 is 424632.
The greatest common factor of 1232/312,1408/8166 = [GCF of 1232,1408]/[LCM of 312,8166]= 176/424632
Therefore, the GCF of 1232/312,1408/8166 is 176/424632.
To find the highest common factor of 1232,1408, we have to find the factors of both numbers and list the highest common factor.
The factors of 1232 are 1, 2, 4, 7, 8, 11, 14, 16, 22, 28, 44, 56, 77, 88, 112, 154, 176, 308, 616, 1232
The factors of 1408 are 1, 2, 4, 8, 11, 16, 22, 32, 44, 64, 88, 128, 176, 352, 704, 1408
The HCF of 1232,1408 is 176.
Lets's calculate GCF of 1232,1408
| 2 | 1232, 1408 |
| 2 | 616, 704 |
| 2 | 308, 352 |
| 2 | 154, 176 |
| 11 | 77, 88 |
| 7, 8 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 2 x 11 = 176
Greatest Common Factor of 1232,1408 By Matching Biggest Common Factor Method
Now, list down the factors of 1232
:1,2,4,7,8,11,14,16,22,28,44,56,77,88,112,154,176,308,616,1232
Now, list down the factors of 1408
:1,2,4,8,11,16,22,32,44,64,88,128,176,352,704,1408
Greatest Common Factor
We found the factors 1232,1408 . The biggest common factor number is the GCF number.
So the greatest common factor 1232,1408 is 176.
Lets's calculate LCM of 312,8166
| 2 | 312, 8166 |
| 3 | 156, 4083 |
| 52, 1361 |
∴ So the LCM of the given numbers is 2 x 3 x 52 x 1361 = 424632
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 176/424632
Therefore, the GCF of Fractions 1232/312,1408/8166 is 176/424632
Least Common Multiple of 312,8166 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 312,8166 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(312,8166) = 6
common factors(in case of two or more numbers have common factors) = 1
GCF(312,8166) x common factors =6 x 1 = 6
LCM(312,8166) = ( 312 × 8166 ) / 6
LCM(312,8166) = 2547792 / 6
LCM(312,8166) = 424632
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FAQs on GCF of Fractions of 1232/312, 1408/8166
1. What is the HCF of 1232,1408?
The HCF of 1232,1408 is 176
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 1232/312, 1408/8166?
Answer: GCF of Numerators as per given numbers 1232/312, 1408/8166 is
GCF of Numerators i.e. for 1232,1408 is 176
LCM of denominators i.e. for 312,8166 is 424632.
Thus, GCF of Fractions is 176/424632.Finally, GCF of Fractions for 1232/312, 1408/8166 is 176/424632.