GCF of 195/42, 646/106
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 195/42, 646/106 i.e 1/2226 easily. The following is the detailed procedure to determine the greatest common factor of fractions 195/42, 646/106.
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 195/42,646/106?
Given fractions are 195/42,646/106
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 195/42,646/106, numerators are 195,646
Denominators are 42,106
The GCF of 195,646 is 1 .
LCM of 42,106 is 2226.
The greatest common factor of 195/42,646/106 = [GCF of 195,646]/[LCM of 42,106]= 1/2226
Therefore, the GCF of 195/42,646/106 is 1/2226.
To find the highest common factor of 195,646, we have to find the factors of both numbers and list the highest common factor.
The factors of 195 are 1, 3, 5, 13, 15, 39, 65, 195
The factors of 646 are 1, 2, 17, 19, 34, 38, 323, 646
The HCF of 195,646 is 1.
Lets's calculate GCF of 195,646
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 195,646 By Matching Biggest Common Factor Method
Now, list down the factors of 195
:1,3,5,13,15,39,65,195
Now, list down the factors of 646
:1,2,17,19,34,38,323,646
Greatest Common Factor
We found the factors 195,646 . The biggest common factor number is the GCF number.
So the greatest common factor 195,646 is 1.
Lets's calculate LCM of 42,106
| 2 | 42, 106 |
| 21, 53 |
∴ So the LCM of the given numbers is 2 x 21 x 53 = 2226
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/2226
Therefore, the GCF of Fractions 195/42,646/106 is 1/2226
Least Common Multiple of 42,106 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 42,106 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(42,106) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(42,106) x common factors =2 x 1 = 2
LCM(42,106) = ( 42 × 106 ) / 2
LCM(42,106) = 4452 / 2
LCM(42,106) = 2226
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FAQs on GCF of Fractions of 195/42, 646/106
1. What is the HCF of 195,646?
The HCF of 195,646 is 1
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 195/42, 646/106?
Answer: GCF of Numerators as per given numbers 195/42, 646/106 is
GCF of Numerators i.e. for 195,646 is 1
LCM of denominators i.e. for 42,106 is 2226.
Thus, GCF of Fractions is 1/2226.Finally, GCF of Fractions for 195/42, 646/106 is 1/2226.