GCF of 123/38, 840/436
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 123/38, 840/436 i.e 3/8284 easily. The following is the detailed procedure to determine the greatest common factor of fractions 123/38, 840/436.
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 123/38,840/436?
Given fractions are 123/38,840/436
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 123/38,840/436, numerators are 123,840
Denominators are 38,436
The GCF of 123,840 is 3 .
LCM of 38,436 is 8284.
The greatest common factor of 123/38,840/436 = [GCF of 123,840]/[LCM of 38,436]= 3/8284
Therefore, the GCF of 123/38,840/436 is 3/8284.
To find the highest common factor of 123,840, we have to find the factors of both numbers and list the highest common factor.
The factors of 123 are 1, 3, 41, 123
The factors of 840 are 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24, 28, 30, 35, 40, 42, 56, 60, 70, 84, 105, 120, 140, 168, 210, 280, 420, 840
The HCF of 123,840 is 3.
Lets's calculate GCF of 123,840
| 3 | 123, 840 |
| 41, 280 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 123,840 By Matching Biggest Common Factor Method
Now, list down the factors of 123
:1,3,41,123
Now, list down the factors of 840
:1,2,3,4,5,6,7,8,10,12,14,15,20,21,24,28,30,35,40,42,56,60,70,84,105,120,140,168,210,280,420,840
Greatest Common Factor
We found the factors 123,840 . The biggest common factor number is the GCF number.
So the greatest common factor 123,840 is 3.
Lets's calculate LCM of 38,436
| 2 | 38, 436 |
| 19, 218 |
∴ So the LCM of the given numbers is 2 x 19 x 218 = 8284
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/8284
Therefore, the GCF of Fractions 123/38,840/436 is 3/8284
Least Common Multiple of 38,436 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 38,436 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(38,436) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(38,436) x common factors =2 x 1 = 2
LCM(38,436) = ( 38 × 436 ) / 2
LCM(38,436) = 16568 / 2
LCM(38,436) = 8284
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FAQs on GCF of Fractions of 123/38, 840/436
1. What is the HCF of 123,840?
The HCF of 123,840 is 3
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 123/38, 840/436?
Answer: GCF of Numerators as per given numbers 123/38, 840/436 is
GCF of Numerators i.e. for 123,840 is 3
LCM of denominators i.e. for 38,436 is 8284.
Thus, GCF of Fractions is 3/8284.Finally, GCF of Fractions for 123/38, 840/436 is 3/8284.