GCF of 119/51, 357/222
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 119/51, 357/222 i.e 119/3774 easily. The following is the detailed procedure to determine the greatest common factor of fractions 119/51, 357/222.
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 119/51,357/222?
Given fractions are 119/51,357/222
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 119/51,357/222, numerators are 119,357
Denominators are 51,222
The GCF of 119,357 is 119 .
LCM of 51,222 is 3774.
The greatest common factor of 119/51,357/222 = [GCF of 119,357]/[LCM of 51,222]= 119/3774
Therefore, the GCF of 119/51,357/222 is 119/3774.
To find the highest common factor of 119,357, we have to find the factors of both numbers and list the highest common factor.
The factors of 119 are 1, 7, 17, 119
The factors of 357 are 1, 3, 7, 17, 21, 51, 119, 357
The HCF of 119,357 is 119.
Lets's calculate GCF of 119,357
| 7 | 119, 357 |
| 17 | 17, 51 |
| 1, 3 |
∴ So the GCF of the given numbers is 7 x 17 = 119
Greatest Common Factor of 119,357 By Matching Biggest Common Factor Method
Now, list down the factors of 119
:1,7,17,119
Now, list down the factors of 357
:1,3,7,17,21,51,119,357
Greatest Common Factor
We found the factors 119,357 . The biggest common factor number is the GCF number.
So the greatest common factor 119,357 is 119.
Lets's calculate LCM of 51,222
| 3 | 51, 222 |
| 17, 74 |
∴ So the LCM of the given numbers is 3 x 17 x 74 = 3774
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 119/3774
Therefore, the GCF of Fractions 119/51,357/222 is 119/3774
Least Common Multiple of 51,222 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 51,222 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(51,222) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(51,222) x common factors =3 x 1 = 3
LCM(51,222) = ( 51 × 222 ) / 3
LCM(51,222) = 11322 / 3
LCM(51,222) = 3774
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FAQs on GCF of Fractions of 119/51, 357/222
1. What is the HCF of 119,357?
The HCF of 119,357 is 119
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 119/51, 357/222?
Answer: GCF of Numerators as per given numbers 119/51, 357/222 is
GCF of Numerators i.e. for 119,357 is 119
LCM of denominators i.e. for 51,222 is 3774.
Thus, GCF of Fractions is 119/3774.Finally, GCF of Fractions for 119/51, 357/222 is 119/3774.