GCF of 874/38, 414/236
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 874/38, 414/236 i.e 46/4484 easily. The following is the detailed procedure to determine the greatest common factor of fractions 874/38, 414/236.
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 874/38,414/236?
Given fractions are 874/38,414/236
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 874/38,414/236, numerators are 874,414
Denominators are 38,236
The GCF of 874,414 is 46 .
LCM of 38,236 is 4484.
The greatest common factor of 874/38,414/236 = [GCF of 874,414]/[LCM of 38,236]= 46/4484
Therefore, the GCF of 874/38,414/236 is 46/4484.
To find the highest common factor of 874,414, we have to find the factors of both numbers and list the highest common factor.
The factors of 874 are 1, 2, 19, 23, 38, 46, 437, 874
The factors of 414 are 1, 2, 3, 6, 9, 18, 23, 46, 69, 138, 207, 414
The HCF of 874,414 is 46.
Lets's calculate GCF of 874,414
| 2 | 874, 414 |
| 23 | 437, 207 |
| 19, 9 |
∴ So the GCF of the given numbers is 2 x 23 = 46
Greatest Common Factor of 874,414 By Matching Biggest Common Factor Method
Now, list down the factors of 874
:1,2,19,23,38,46,437,874
Now, list down the factors of 414
:1,2,3,6,9,18,23,46,69,138,207,414
Greatest Common Factor
We found the factors 874,414 . The biggest common factor number is the GCF number.
So the greatest common factor 874,414 is 46.
Lets's calculate LCM of 38,236
| 2 | 38, 236 |
| 19, 118 |
∴ So the LCM of the given numbers is 2 x 19 x 118 = 4484
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 46/4484
Therefore, the GCF of Fractions 874/38,414/236 is 46/4484
Least Common Multiple of 38,236 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 38,236 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(38,236) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(38,236) x common factors =2 x 1 = 2
LCM(38,236) = ( 38 × 236 ) / 2
LCM(38,236) = 8968 / 2
LCM(38,236) = 4484
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FAQs on GCF of Fractions of 874/38, 414/236
1. What is the HCF of 874,414?
The HCF of 874,414 is 46
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 874/38, 414/236?
Answer: GCF of Numerators as per given numbers 874/38, 414/236 is
GCF of Numerators i.e. for 874,414 is 46
LCM of denominators i.e. for 38,236 is 4484.
Thus, GCF of Fractions is 46/4484.Finally, GCF of Fractions for 874/38, 414/236 is 46/4484.