GCF of 406/42, 232/154
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 406/42, 232/154 i.e 58/462 easily. The following is the detailed procedure to determine the greatest common factor of fractions 406/42, 232/154.
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 406/42,232/154?
Given fractions are 406/42,232/154
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 406/42,232/154, numerators are 406,232
Denominators are 42,154
The GCF of 406,232 is 58 .
LCM of 42,154 is 462.
The greatest common factor of 406/42,232/154 = [GCF of 406,232]/[LCM of 42,154]= 58/462
Therefore, the GCF of 406/42,232/154 is 58/462.
To find the highest common factor of 406,232, we have to find the factors of both numbers and list the highest common factor.
The factors of 406 are 1, 2, 7, 14, 29, 58, 203, 406
The factors of 232 are 1, 2, 4, 8, 29, 58, 116, 232
The HCF of 406,232 is 58.
Lets's calculate GCF of 406,232
| 2 | 406, 232 |
| 29 | 203, 116 |
| 7, 4 |
∴ So the GCF of the given numbers is 2 x 29 = 58
Greatest Common Factor of 406,232 By Matching Biggest Common Factor Method
Now, list down the factors of 406
:1,2,7,14,29,58,203,406
Now, list down the factors of 232
:1,2,4,8,29,58,116,232
Greatest Common Factor
We found the factors 406,232 . The biggest common factor number is the GCF number.
So the greatest common factor 406,232 is 58.
Lets's calculate LCM of 42,154
| 2 | 42, 154 |
| 7 | 21, 77 |
| 3, 11 |
∴ So the LCM of the given numbers is 2 x 7 x 3 x 11 = 462
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 58/462
Therefore, the GCF of Fractions 406/42,232/154 is 58/462
Least Common Multiple of 42,154 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 42,154 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(42,154) = 14
common factors(in case of two or more numbers have common factors) = 1
GCF(42,154) x common factors =14 x 1 = 14
LCM(42,154) = ( 42 × 154 ) / 14
LCM(42,154) = 6468 / 14
LCM(42,154) = 462
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FAQs on GCF of Fractions of 406/42, 232/154
1. What is the HCF of 406,232?
The HCF of 406,232 is 58
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 406/42, 232/154?
Answer: GCF of Numerators as per given numbers 406/42, 232/154 is
GCF of Numerators i.e. for 406,232 is 58
LCM of denominators i.e. for 42,154 is 462.
Thus, GCF of Fractions is 58/462.Finally, GCF of Fractions for 406/42, 232/154 is 58/462.