GCF of 224/382, 786/409
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 224/382, 786/409 i.e 2/156238 easily. The following is the detailed procedure to determine the greatest common factor of fractions 224/382, 786/409.
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 224/382,786/409?
Given fractions are 224/382,786/409
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 224/382,786/409, numerators are 224,786
Denominators are 382,409
The GCF of 224,786 is 2 .
LCM of 382,409 is 156238.
The greatest common factor of 224/382,786/409 = [GCF of 224,786]/[LCM of 382,409]= 2/156238
Therefore, the GCF of 224/382,786/409 is 2/156238.
To find the highest common factor of 224,786, we have to find the factors of both numbers and list the highest common factor.
The factors of 224 are 1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 112, 224
The factors of 786 are 1, 2, 3, 6, 131, 262, 393, 786
The HCF of 224,786 is 2.
Lets's calculate GCF of 224,786
| 2 | 224, 786 |
| 112, 393 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 224,786 By Matching Biggest Common Factor Method
Now, list down the factors of 224
:1,2,4,7,8,14,16,28,32,56,112,224
Now, list down the factors of 786
:1,2,3,6,131,262,393,786
Greatest Common Factor
We found the factors 224,786 . The biggest common factor number is the GCF number.
So the greatest common factor 224,786 is 2.
Lets's calculate LCM of 382,409
Given numbers has no common factors except 1. So, there LCM is their product i.e 156238
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/156238
Therefore, the GCF of Fractions 224/382,786/409 is 2/156238
Least Common Multiple of 382,409 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 382,409 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(382,409) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(382,409) x common factors =1 x 1 = 1
LCM(382,409) = ( 382 × 409 ) / 1
LCM(382,409) = 156238 / 1
LCM(382,409) = 156238
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FAQs on GCF of Fractions of 224/382, 786/409
1. What is the HCF of 224,786?
The HCF of 224,786 is 2
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 224/382, 786/409?
Answer: GCF of Numerators as per given numbers 224/382, 786/409 is
GCF of Numerators i.e. for 224,786 is 2
LCM of denominators i.e. for 382,409 is 156238.
Thus, GCF of Fractions is 2/156238.Finally, GCF of Fractions for 224/382, 786/409 is 2/156238.