GCF of 284/409, 1278/651
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 284/409, 1278/651 i.e 142/266259 easily. The following is the detailed procedure to determine the greatest common factor of fractions 284/409, 1278/651.
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 284/409,1278/651?
Given fractions are 284/409,1278/651
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 284/409,1278/651, numerators are 284,1278
Denominators are 409,651
The GCF of 284,1278 is 142 .
LCM of 409,651 is 266259.
The greatest common factor of 284/409,1278/651 = [GCF of 284,1278]/[LCM of 409,651]= 142/266259
Therefore, the GCF of 284/409,1278/651 is 142/266259.
To find the highest common factor of 284,1278, we have to find the factors of both numbers and list the highest common factor.
The factors of 284 are 1, 2, 4, 71, 142, 284
The factors of 1278 are 1, 2, 3, 6, 9, 18, 71, 142, 213, 426, 639, 1278
The HCF of 284,1278 is 142.
Lets's calculate GCF of 284,1278
| 2 | 284, 1278 |
| 71 | 142, 639 |
| 2, 9 |
∴ So the GCF of the given numbers is 2 x 71 = 142
Greatest Common Factor of 284,1278 By Matching Biggest Common Factor Method
Now, list down the factors of 284
:1,2,4,71,142,284
Now, list down the factors of 1278
:1,2,3,6,9,18,71,142,213,426,639,1278
Greatest Common Factor
We found the factors 284,1278 . The biggest common factor number is the GCF number.
So the greatest common factor 284,1278 is 142.
Lets's calculate LCM of 409,651
Given numbers has no common factors except 1. So, there LCM is their product i.e 266259
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 142/266259
Therefore, the GCF of Fractions 284/409,1278/651 is 142/266259
Least Common Multiple of 409,651 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 409,651 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(409,651) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(409,651) x common factors =1 x 1 = 1
LCM(409,651) = ( 409 × 651 ) / 1
LCM(409,651) = 266259 / 1
LCM(409,651) = 266259
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FAQs on GCF of Fractions of 284/409, 1278/651
1. What is the HCF of 284,1278?
The HCF of 284,1278 is 142
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 284/409, 1278/651?
Answer: GCF of Numerators as per given numbers 284/409, 1278/651 is
GCF of Numerators i.e. for 284,1278 is 142
LCM of denominators i.e. for 409,651 is 266259.
Thus, GCF of Fractions is 142/266259.Finally, GCF of Fractions for 284/409, 1278/651 is 142/266259.