GCF of 382/32, 2114/257
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 382/32, 2114/257 i.e 2/8224 easily. The following is the detailed procedure to determine the greatest common factor of fractions 382/32, 2114/257.
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 382/32,2114/257?
Given fractions are 382/32,2114/257
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 382/32,2114/257, numerators are 382,2114
Denominators are 32,257
The GCF of 382,2114 is 2 .
LCM of 32,257 is 8224.
The greatest common factor of 382/32,2114/257 = [GCF of 382,2114]/[LCM of 32,257]= 2/8224
Therefore, the GCF of 382/32,2114/257 is 2/8224.
To find the highest common factor of 382,2114, we have to find the factors of both numbers and list the highest common factor.
The factors of 382 are 1, 2, 191, 382
The factors of 2114 are 1, 2, 7, 14, 151, 302, 1057, 2114
The HCF of 382,2114 is 2.
Lets's calculate GCF of 382,2114
| 2 | 382, 2114 |
| 191, 1057 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 382,2114 By Matching Biggest Common Factor Method
Now, list down the factors of 382
:1,2,191,382
Now, list down the factors of 2114
:1,2,7,14,151,302,1057,2114
Greatest Common Factor
We found the factors 382,2114 . The biggest common factor number is the GCF number.
So the greatest common factor 382,2114 is 2.
Lets's calculate LCM of 32,257
Given numbers has no common factors except 1. So, there LCM is their product i.e 8224
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/8224
Therefore, the GCF of Fractions 382/32,2114/257 is 2/8224
Least Common Multiple of 32,257 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 32,257 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(32,257) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(32,257) x common factors =1 x 1 = 1
LCM(32,257) = ( 32 × 257 ) / 1
LCM(32,257) = 8224 / 1
LCM(32,257) = 8224
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FAQs on GCF of Fractions of 382/32, 2114/257
1. What is the HCF of 382,2114?
The HCF of 382,2114 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 382/32, 2114/257?
Answer: GCF of Numerators as per given numbers 382/32, 2114/257 is
GCF of Numerators i.e. for 382,2114 is 2
LCM of denominators i.e. for 32,257 is 8224.
Thus, GCF of Fractions is 2/8224.Finally, GCF of Fractions for 382/32, 2114/257 is 2/8224.