GCF of 814/282, 176/354
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 814/282, 176/354 i.e 22/16638 easily. The following is the detailed procedure to determine the greatest common factor of fractions 814/282, 176/354.
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 814/282,176/354?
Given fractions are 814/282,176/354
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 814/282,176/354, numerators are 814,176
Denominators are 282,354
The GCF of 814,176 is 22 .
LCM of 282,354 is 16638.
The greatest common factor of 814/282,176/354 = [GCF of 814,176]/[LCM of 282,354]= 22/16638
Therefore, the GCF of 814/282,176/354 is 22/16638.
To find the highest common factor of 814,176, we have to find the factors of both numbers and list the highest common factor.
The factors of 814 are 1, 2, 11, 22, 37, 74, 407, 814
The factors of 176 are 1, 2, 4, 8, 11, 16, 22, 44, 88, 176
The HCF of 814,176 is 22.
Lets's calculate GCF of 814,176
| 2 | 814, 176 |
| 11 | 407, 88 |
| 37, 8 |
∴ So the GCF of the given numbers is 2 x 11 = 22
Greatest Common Factor of 814,176 By Matching Biggest Common Factor Method
Now, list down the factors of 814
:1,2,11,22,37,74,407,814
Now, list down the factors of 176
:1,2,4,8,11,16,22,44,88,176
Greatest Common Factor
We found the factors 814,176 . The biggest common factor number is the GCF number.
So the greatest common factor 814,176 is 22.
Lets's calculate LCM of 282,354
| 2 | 282, 354 |
| 3 | 141, 177 |
| 47, 59 |
∴ So the LCM of the given numbers is 2 x 3 x 47 x 59 = 16638
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 22/16638
Therefore, the GCF of Fractions 814/282,176/354 is 22/16638
Least Common Multiple of 282,354 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 282,354 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(282,354) = 6
common factors(in case of two or more numbers have common factors) = 1
GCF(282,354) x common factors =6 x 1 = 6
LCM(282,354) = ( 282 × 354 ) / 6
LCM(282,354) = 99828 / 6
LCM(282,354) = 16638
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FAQs on GCF of Fractions of 814/282, 176/354
1. What is the HCF of 814,176?
The HCF of 814,176 is 22
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 814/282, 176/354?
Answer: GCF of Numerators as per given numbers 814/282, 176/354 is
GCF of Numerators i.e. for 814,176 is 22
LCM of denominators i.e. for 282,354 is 16638.
Thus, GCF of Fractions is 22/16638.Finally, GCF of Fractions for 814/282, 176/354 is 22/16638.