GCF of 145/69, 474/312
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 145/69, 474/312 i.e 1/7176 easily. The following is the detailed procedure to determine the greatest common factor of fractions 145/69, 474/312.
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 145/69,474/312?
Given fractions are 145/69,474/312
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 145/69,474/312, numerators are 145,474
Denominators are 69,312
The GCF of 145,474 is 1 .
LCM of 69,312 is 7176.
The greatest common factor of 145/69,474/312 = [GCF of 145,474]/[LCM of 69,312]= 1/7176
Therefore, the GCF of 145/69,474/312 is 1/7176.
To find the highest common factor of 145,474, we have to find the factors of both numbers and list the highest common factor.
The factors of 145 are 1, 5, 29, 145
The factors of 474 are 1, 2, 3, 6, 79, 158, 237, 474
The HCF of 145,474 is 1.
Lets's calculate GCF of 145,474
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 145,474 By Matching Biggest Common Factor Method
Now, list down the factors of 145
:1,5,29,145
Now, list down the factors of 474
:1,2,3,6,79,158,237,474
Greatest Common Factor
We found the factors 145,474 . The biggest common factor number is the GCF number.
So the greatest common factor 145,474 is 1.
Lets's calculate LCM of 69,312
| 3 | 69, 312 |
| 23, 104 |
∴ So the LCM of the given numbers is 3 x 23 x 104 = 7176
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/7176
Therefore, the GCF of Fractions 145/69,474/312 is 1/7176
Least Common Multiple of 69,312 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 69,312 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(69,312) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(69,312) x common factors =3 x 1 = 3
LCM(69,312) = ( 69 × 312 ) / 3
LCM(69,312) = 21528 / 3
LCM(69,312) = 7176
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FAQs on GCF of Fractions of 145/69, 474/312
1. What is the HCF of 145,474?
The HCF of 145,474 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 145/69, 474/312?
Answer: GCF of Numerators as per given numbers 145/69, 474/312 is
GCF of Numerators i.e. for 145,474 is 1
LCM of denominators i.e. for 69,312 is 7176.
Thus, GCF of Fractions is 1/7176.Finally, GCF of Fractions for 145/69, 474/312 is 1/7176.