GCF of 105/382, 567/974
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 105/382, 567/974 i.e 21/186034 easily. The following is the detailed procedure to determine the greatest common factor of fractions 105/382, 567/974.
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 105/382,567/974?
Given fractions are 105/382,567/974
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 105/382,567/974, numerators are 105,567
Denominators are 382,974
The GCF of 105,567 is 21 .
LCM of 382,974 is 186034.
The greatest common factor of 105/382,567/974 = [GCF of 105,567]/[LCM of 382,974]= 21/186034
Therefore, the GCF of 105/382,567/974 is 21/186034.
To find the highest common factor of 105,567, we have to find the factors of both numbers and list the highest common factor.
The factors of 105 are 1, 3, 5, 7, 15, 21, 35, 105
The factors of 567 are 1, 3, 7, 9, 21, 27, 63, 81, 189, 567
The HCF of 105,567 is 21.
Lets's calculate GCF of 105,567
| 3 | 105, 567 |
| 7 | 35, 189 |
| 5, 27 |
∴ So the GCF of the given numbers is 3 x 7 = 21
Greatest Common Factor of 105,567 By Matching Biggest Common Factor Method
Now, list down the factors of 105
:1,3,5,7,15,21,35,105
Now, list down the factors of 567
:1,3,7,9,21,27,63,81,189,567
Greatest Common Factor
We found the factors 105,567 . The biggest common factor number is the GCF number.
So the greatest common factor 105,567 is 21.
Lets's calculate LCM of 382,974
| 2 | 382, 974 |
| 191, 487 |
∴ So the LCM of the given numbers is 2 x 191 x 487 = 186034
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 21/186034
Therefore, the GCF of Fractions 105/382,567/974 is 21/186034
Least Common Multiple of 382,974 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 382,974 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(382,974) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(382,974) x common factors =2 x 1 = 2
LCM(382,974) = ( 382 × 974 ) / 2
LCM(382,974) = 372068 / 2
LCM(382,974) = 186034
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FAQs on GCF of Fractions of 105/382, 567/974
1. What is the HCF of 105,567?
The HCF of 105,567 is 21
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 105/382, 567/974?
Answer: GCF of Numerators as per given numbers 105/382, 567/974 is
GCF of Numerators i.e. for 105,567 is 21
LCM of denominators i.e. for 382,974 is 186034.
Thus, GCF of Fractions is 21/186034.Finally, GCF of Fractions for 105/382, 567/974 is 21/186034.