GCF of 145/74, 612/284
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 145/74, 612/284 i.e 1/10508 easily. The following is the detailed procedure to determine the greatest common factor of fractions 145/74, 612/284.
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 145/74,612/284?
Given fractions are 145/74,612/284
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 145/74,612/284, numerators are 145,612
Denominators are 74,284
The GCF of 145,612 is 1 .
LCM of 74,284 is 10508.
The greatest common factor of 145/74,612/284 = [GCF of 145,612]/[LCM of 74,284]= 1/10508
Therefore, the GCF of 145/74,612/284 is 1/10508.
To find the highest common factor of 145,612, 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 612 are 1, 2, 3, 4, 6, 9, 12, 17, 18, 34, 36, 51, 68, 102, 153, 204, 306, 612
The HCF of 145,612 is 1.
Lets's calculate GCF of 145,612
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 145,612 By Matching Biggest Common Factor Method
Now, list down the factors of 145
:1,5,29,145
Now, list down the factors of 612
:1,2,3,4,6,9,12,17,18,34,36,51,68,102,153,204,306,612
Greatest Common Factor
We found the factors 145,612 . The biggest common factor number is the GCF number.
So the greatest common factor 145,612 is 1.
Lets's calculate LCM of 74,284
| 2 | 74, 284 |
| 37, 142 |
∴ So the LCM of the given numbers is 2 x 37 x 142 = 10508
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/10508
Therefore, the GCF of Fractions 145/74,612/284 is 1/10508
Least Common Multiple of 74,284 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 74,284 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(74,284) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(74,284) x common factors =2 x 1 = 2
LCM(74,284) = ( 74 × 284 ) / 2
LCM(74,284) = 21016 / 2
LCM(74,284) = 10508
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FAQs on GCF of Fractions of 145/74, 612/284
1. What is the HCF of 145,612?
The HCF of 145,612 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 145/74, 612/284?
Answer: GCF of Numerators as per given numbers 145/74, 612/284 is
GCF of Numerators i.e. for 145,612 is 1
LCM of denominators i.e. for 74,284 is 10508.
Thus, GCF of Fractions is 1/10508.Finally, GCF of Fractions for 145/74, 612/284 is 1/10508.