GCF of 476/408, 678/870
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 476/408, 678/870 i.e 2/59160 easily. The following is the detailed procedure to determine the greatest common factor of fractions 476/408, 678/870.
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 476/408,678/870?
Given fractions are 476/408,678/870
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 476/408,678/870, numerators are 476,678
Denominators are 408,870
The GCF of 476,678 is 2 .
LCM of 408,870 is 59160.
The greatest common factor of 476/408,678/870 = [GCF of 476,678]/[LCM of 408,870]= 2/59160
Therefore, the GCF of 476/408,678/870 is 2/59160.
To find the highest common factor of 476,678, we have to find the factors of both numbers and list the highest common factor.
The factors of 476 are 1, 2, 4, 7, 14, 17, 28, 34, 68, 119, 238, 476
The factors of 678 are 1, 2, 3, 6, 113, 226, 339, 678
The HCF of 476,678 is 2.
Lets's calculate GCF of 476,678
| 2 | 476, 678 |
| 238, 339 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 476,678 By Matching Biggest Common Factor Method
Now, list down the factors of 476
:1,2,4,7,14,17,28,34,68,119,238,476
Now, list down the factors of 678
:1,2,3,6,113,226,339,678
Greatest Common Factor
We found the factors 476,678 . The biggest common factor number is the GCF number.
So the greatest common factor 476,678 is 2.
Lets's calculate LCM of 408,870
| 2 | 408, 870 |
| 3 | 204, 435 |
| 68, 145 |
∴ So the LCM of the given numbers is 2 x 3 x 68 x 145 = 59160
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/59160
Therefore, the GCF of Fractions 476/408,678/870 is 2/59160
Least Common Multiple of 408,870 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 408,870 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(408,870) = 6
common factors(in case of two or more numbers have common factors) = 1
GCF(408,870) x common factors =6 x 1 = 6
LCM(408,870) = ( 408 × 870 ) / 6
LCM(408,870) = 354960 / 6
LCM(408,870) = 59160
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FAQs on GCF of Fractions of 476/408, 678/870
1. What is the HCF of 476,678?
The HCF of 476,678 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 476/408, 678/870?
Answer: GCF of Numerators as per given numbers 476/408, 678/870 is
GCF of Numerators i.e. for 476,678 is 2
LCM of denominators i.e. for 408,870 is 59160.
Thus, GCF of Fractions is 2/59160.Finally, GCF of Fractions for 476/408, 678/870 is 2/59160.