GCF of 183/42, 420/8394
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 183/42, 420/8394 i.e 3/58758 easily. The following is the detailed procedure to determine the greatest common factor of fractions 183/42, 420/8394.
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 183/42,420/8394?
Given fractions are 183/42,420/8394
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 183/42,420/8394, numerators are 183,420
Denominators are 42,8394
The GCF of 183,420 is 3 .
LCM of 42,8394 is 58758.
The greatest common factor of 183/42,420/8394 = [GCF of 183,420]/[LCM of 42,8394]= 3/58758
Therefore, the GCF of 183/42,420/8394 is 3/58758.
To find the highest common factor of 183,420, we have to find the factors of both numbers and list the highest common factor.
The factors of 183 are 1, 3, 61, 183
The factors of 420 are 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, 420
The HCF of 183,420 is 3.
Lets's calculate GCF of 183,420
| 3 | 183, 420 |
| 61, 140 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 183,420 By Matching Biggest Common Factor Method
Now, list down the factors of 183
:1,3,61,183
Now, list down the factors of 420
:1,2,3,4,5,6,7,10,12,14,15,20,21,28,30,35,42,60,70,84,105,140,210,420
Greatest Common Factor
We found the factors 183,420 . The biggest common factor number is the GCF number.
So the greatest common factor 183,420 is 3.
Lets's calculate LCM of 42,8394
| 2 | 42, 8394 |
| 3 | 21, 4197 |
| 7, 1399 |
∴ So the LCM of the given numbers is 2 x 3 x 7 x 1399 = 58758
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/58758
Therefore, the GCF of Fractions 183/42,420/8394 is 3/58758
Least Common Multiple of 42,8394 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 42,8394 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(42,8394) = 6
common factors(in case of two or more numbers have common factors) = 1
GCF(42,8394) x common factors =6 x 1 = 6
LCM(42,8394) = ( 42 × 8394 ) / 6
LCM(42,8394) = 352548 / 6
LCM(42,8394) = 58758
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FAQs on GCF of Fractions of 183/42, 420/8394
1. What is the HCF of 183,420?
The HCF of 183,420 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 183/42, 420/8394?
Answer: GCF of Numerators as per given numbers 183/42, 420/8394 is
GCF of Numerators i.e. for 183,420 is 3
LCM of denominators i.e. for 42,8394 is 58758.
Thus, GCF of Fractions is 3/58758.Finally, GCF of Fractions for 183/42, 420/8394 is 3/58758.