GCF of 824/12, 874/3678
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 824/12, 874/3678 i.e 2/7356 easily. The following is the detailed procedure to determine the greatest common factor of fractions 824/12, 874/3678.
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 824/12,874/3678?
Given fractions are 824/12,874/3678
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 824/12,874/3678, numerators are 824,874
Denominators are 12,3678
The GCF of 824,874 is 2 .
LCM of 12,3678 is 7356.
The greatest common factor of 824/12,874/3678 = [GCF of 824,874]/[LCM of 12,3678]= 2/7356
Therefore, the GCF of 824/12,874/3678 is 2/7356.
To find the highest common factor of 824,874, we have to find the factors of both numbers and list the highest common factor.
The factors of 824 are 1, 2, 4, 8, 103, 206, 412, 824
The factors of 874 are 1, 2, 19, 23, 38, 46, 437, 874
The HCF of 824,874 is 2.
Lets's calculate GCF of 824,874
| 2 | 824, 874 |
| 412, 437 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 824,874 By Matching Biggest Common Factor Method
Now, list down the factors of 824
:1,2,4,8,103,206,412,824
Now, list down the factors of 874
:1,2,19,23,38,46,437,874
Greatest Common Factor
We found the factors 824,874 . The biggest common factor number is the GCF number.
So the greatest common factor 824,874 is 2.
Lets's calculate LCM of 12,3678
| 2 | 12, 3678 |
| 3 | 6, 1839 |
| 2, 613 |
∴ So the LCM of the given numbers is 2 x 3 x 2 x 613 = 7356
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/7356
Therefore, the GCF of Fractions 824/12,874/3678 is 2/7356
Least Common Multiple of 12,3678 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 12,3678 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(12,3678) = 6
common factors(in case of two or more numbers have common factors) = 1
GCF(12,3678) x common factors =6 x 1 = 6
LCM(12,3678) = ( 12 × 3678 ) / 6
LCM(12,3678) = 44136 / 6
LCM(12,3678) = 7356
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FAQs on GCF of Fractions of 824/12, 874/3678
1. What is the HCF of 824,874?
The HCF of 824,874 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 824/12, 874/3678?
Answer: GCF of Numerators as per given numbers 824/12, 874/3678 is
GCF of Numerators i.e. for 824,874 is 2
LCM of denominators i.e. for 12,3678 is 7356.
Thus, GCF of Fractions is 2/7356.Finally, GCF of Fractions for 824/12, 874/3678 is 2/7356.