GCF of 37/84, 260/70, 512/123
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 37/84, 260/70, 512/123 i.e 1/17220 easily. The following is the detailed procedure to determine the greatest common factor of fractions 37/84, 260/70, 512/123.
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 37/84,260/70,512/123?
Given fractions are 37/84,260/70,512/123
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 37/84,260/70,512/123, numerators are 37,260,512
Denominators are 84,70,123
The GCF of 37,260,512 is 1 .
LCM of 84,70,123 is 17220.
The greatest common factor of 37/84,260/70,512/123 = [GCF of 37,260,512]/[LCM of 84,70,123]= 1/17220
Therefore, the GCF of 37/84,260/70,512/123 is 1/17220.
To find the highest common factor of 37,260,512, we have to find the factors of both numbers and list the highest common factor.
The factors of 37 are 1, 37
The factors of 260 are 1, 2, 4, 5, 10, 13, 20, 26, 52, 65, 130, 260
The factors of 512 are 1, 2, 4, 8, 16, 32, 64, 128, 256, 512
The HCF of 37,260,512 is 1.
Lets's calculate GCF of 37,260,512
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 37,260,512 By Matching Biggest Common Factor Method
Now, list down the factors of 37
:1,37
Now, list down the factors of 260
:1,2,4,5,10,13,20,26,52,65,130,260
Now, list down the factors of 512
:1,2,4,8,16,32,64,128,256,512
Greatest Common Factor
We found the factors 37,260,512 . The biggest common factor number is the GCF number.
So the greatest common factor 37,260,512 is 1.
Lets's calculate LCM of 84,70,123
| 2 | 84, 70, 123 |
| 3 | 42, 35, 123 |
| 7 | 14, 35, 41 |
| 2, 5, 41 |
∴ So the LCM of the given numbers is 2 x 3 x 7 x 2 x 5 x 41 = 17220
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/17220
Therefore, the GCF of Fractions 37/84,260/70,512/123 is 1/17220
Least Common Multiple of 84,70,123 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 84,70,123 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(84,70,123) = 1
common factors(in case of two or more numbers have common factors) = 42
GCF(84,70,123) x common factors =1 x 42 = 42
LCM(84,70,123) = ( 84 × 70 × 123 ) / 42
LCM(84,70,123) = 723240 / 42
LCM(84,70,123) = 17220
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FAQs on GCF of Fractions of 37/84, 260/70, 512/123
1. What is the HCF of 37,260,512?
The HCF of 37,260,512 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 37/84, 260/70, 512/123?
Answer: GCF of Numerators as per given numbers 37/84, 260/70, 512/123 is
GCF of Numerators i.e. for 37,260,512 is 1
LCM of denominators i.e. for 84,70,123 is 17220.
Thus, GCF of Fractions is 1/17220.Finally, GCF of Fractions for 37/84, 260/70, 512/123 is 1/17220.