GCF of 74/145, 12/414, 312/463
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 74/145, 12/414, 312/463 i.e 2/27793890 easily. The following is the detailed procedure to determine the greatest common factor of fractions 74/145, 12/414, 312/463.
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 74/145,12/414,312/463?
Given fractions are 74/145,12/414,312/463
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 74/145,12/414,312/463, numerators are 74,12,312
Denominators are 145,414,463
The GCF of 74,12,312 is 2 .
LCM of 145,414,463 is 27793890.
The greatest common factor of 74/145,12/414,312/463 = [GCF of 74,12,312]/[LCM of 145,414,463]= 2/27793890
Therefore, the GCF of 74/145,12/414,312/463 is 2/27793890.
To find the highest common factor of 74,12,312, we have to find the factors of both numbers and list the highest common factor.
The factors of 74 are 1, 2, 37, 74
The factors of 12 are 1, 2, 3, 4, 6, 12
The factors of 312 are 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, 312
The HCF of 74,12,312 is 2.
Lets's calculate GCF of 74,12,312
| 2 | 74, 12, 312 |
| 37, 6, 156 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 74,12,312 By Matching Biggest Common Factor Method
Now, list down the factors of 74
:1,2,37,74
Now, list down the factors of 12
:1,2,3,4,6,12
Now, list down the factors of 312
:1,2,3,4,6,8,12,13,24,26,39,52,78,104,156,312
Greatest Common Factor
We found the factors 74,12,312 . The biggest common factor number is the GCF number.
So the greatest common factor 74,12,312 is 2.
Lets's calculate LCM of 145,414,463
Given numbers has no common factors except 1. So, there LCM is their product i.e 27793890
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/27793890
Therefore, the GCF of Fractions 74/145,12/414,312/463 is 2/27793890
Least Common Multiple of 145,414,463 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 145,414,463 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(145,414,463) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(145,414,463) x common factors =1 x 1 = 1
LCM(145,414,463) = ( 145 × 414 × 463 ) / 1
LCM(145,414,463) = 27793890 / 1
LCM(145,414,463) = 27793890
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FAQs on GCF of Fractions of 74/145, 12/414, 312/463
1. What is the HCF of 74,12,312?
The HCF of 74,12,312 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 74/145, 12/414, 312/463?
Answer: GCF of Numerators as per given numbers 74/145, 12/414, 312/463 is
GCF of Numerators i.e. for 74,12,312 is 2
LCM of denominators i.e. for 145,414,463 is 27793890.
Thus, GCF of Fractions is 2/27793890.Finally, GCF of Fractions for 74/145, 12/414, 312/463 is 2/27793890.