GCF of 422/59, 154/30, 318/59
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 422/59, 154/30, 318/59 i.e 2/1770 easily. The following is the detailed procedure to determine the greatest common factor of fractions 422/59, 154/30, 318/59.
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 422/59,154/30,318/59?
Given fractions are 422/59,154/30,318/59
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 422/59,154/30,318/59, numerators are 422,154,318
Denominators are 59,30,59
The GCF of 422,154,318 is 2 .
LCM of 59,30,59 is 1770.
The greatest common factor of 422/59,154/30,318/59 = [GCF of 422,154,318]/[LCM of 59,30,59]= 2/1770
Therefore, the GCF of 422/59,154/30,318/59 is 2/1770.
To find the highest common factor of 422,154,318, we have to find the factors of both numbers and list the highest common factor.
The factors of 422 are 1, 2, 211, 422
The factors of 154 are 1, 2, 7, 11, 14, 22, 77, 154
The factors of 318 are 1, 2, 3, 6, 53, 106, 159, 318
The HCF of 422,154,318 is 2.
Lets's calculate GCF of 422,154,318
| 2 | 422, 154, 318 |
| 211, 77, 159 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 422,154,318 By Matching Biggest Common Factor Method
Now, list down the factors of 422
:1,2,211,422
Now, list down the factors of 154
:1,2,7,11,14,22,77,154
Now, list down the factors of 318
:1,2,3,6,53,106,159,318
Greatest Common Factor
We found the factors 422,154,318 . The biggest common factor number is the GCF number.
So the greatest common factor 422,154,318 is 2.
Lets's calculate LCM of 59,30,59
| 59 | 59, 30, 59 |
| 1, 30, 1 |
∴ So the LCM of the given numbers is 59 x 1 x 30 x 1 = 1770
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/1770
Therefore, the GCF of Fractions 422/59,154/30,318/59 is 2/1770
Least Common Multiple of 59,30,59 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 59,30,59 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(59,30,59) = 1
common factors(in case of two or more numbers have common factors) = 59
GCF(59,30,59) x common factors =1 x 59 = 59
LCM(59,30,59) = ( 59 × 30 × 59 ) / 59
LCM(59,30,59) = 104430 / 59
LCM(59,30,59) = 1770
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FAQs on GCF of Fractions of 422/59, 154/30, 318/59
1. What is the HCF of 422,154,318?
The HCF of 422,154,318 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 422/59, 154/30, 318/59?
Answer: GCF of Numerators as per given numbers 422/59, 154/30, 318/59 is
GCF of Numerators i.e. for 422,154,318 is 2
LCM of denominators i.e. for 59,30,59 is 1770.
Thus, GCF of Fractions is 2/1770.Finally, GCF of Fractions for 422/59, 154/30, 318/59 is 2/1770.