GCF of 994/32, 420/329
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 994/32, 420/329 i.e 14/10528 easily. The following is the detailed procedure to determine the greatest common factor of fractions 994/32, 420/329.
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 994/32,420/329?
Given fractions are 994/32,420/329
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 994/32,420/329, numerators are 994,420
Denominators are 32,329
The GCF of 994,420 is 14 .
LCM of 32,329 is 10528.
The greatest common factor of 994/32,420/329 = [GCF of 994,420]/[LCM of 32,329]= 14/10528
Therefore, the GCF of 994/32,420/329 is 14/10528.
To find the highest common factor of 994,420, we have to find the factors of both numbers and list the highest common factor.
The factors of 994 are 1, 2, 7, 14, 71, 142, 497, 994
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 994,420 is 14.
Lets's calculate GCF of 994,420
| 2 | 994, 420 |
| 7 | 497, 210 |
| 71, 30 |
∴ So the GCF of the given numbers is 2 x 7 = 14
Greatest Common Factor of 994,420 By Matching Biggest Common Factor Method
Now, list down the factors of 994
:1,2,7,14,71,142,497,994
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 994,420 . The biggest common factor number is the GCF number.
So the greatest common factor 994,420 is 14.
Lets's calculate LCM of 32,329
Given numbers has no common factors except 1. So, there LCM is their product i.e 10528
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 14/10528
Therefore, the GCF of Fractions 994/32,420/329 is 14/10528
Least Common Multiple of 32,329 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 32,329 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(32,329) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(32,329) x common factors =1 x 1 = 1
LCM(32,329) = ( 32 × 329 ) / 1
LCM(32,329) = 10528 / 1
LCM(32,329) = 10528
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FAQs on GCF of Fractions of 994/32, 420/329
1. What is the HCF of 994,420?
The HCF of 994,420 is 14
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 994/32, 420/329?
Answer: GCF of Numerators as per given numbers 994/32, 420/329 is
GCF of Numerators i.e. for 994,420 is 14
LCM of denominators i.e. for 32,329 is 10528.
Thus, GCF of Fractions is 14/10528.Finally, GCF of Fractions for 994/32, 420/329 is 14/10528.