GCF of 1762/216, 1858/284
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1762/216, 1858/284 i.e 2/15336 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1762/216, 1858/284.
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 1762/216,1858/284?
Given fractions are 1762/216,1858/284
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 1762/216,1858/284, numerators are 1762,1858
Denominators are 216,284
The GCF of 1762,1858 is 2 .
LCM of 216,284 is 15336.
The greatest common factor of 1762/216,1858/284 = [GCF of 1762,1858]/[LCM of 216,284]= 2/15336
Therefore, the GCF of 1762/216,1858/284 is 2/15336.
To find the highest common factor of 1762,1858, we have to find the factors of both numbers and list the highest common factor.
The factors of 1762 are 1, 2, 881, 1762
The factors of 1858 are 1, 2, 929, 1858
The HCF of 1762,1858 is 2.
Lets's calculate GCF of 1762,1858
| 2 | 1762, 1858 |
| 881, 929 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 1762,1858 By Matching Biggest Common Factor Method
Now, list down the factors of 1762
:1,2,881,1762
Now, list down the factors of 1858
:1,2,929,1858
Greatest Common Factor
We found the factors 1762,1858 . The biggest common factor number is the GCF number.
So the greatest common factor 1762,1858 is 2.
Lets's calculate LCM of 216,284
| 2 | 216, 284 |
| 2 | 108, 142 |
| 54, 71 |
∴ So the LCM of the given numbers is 2 x 2 x 54 x 71 = 15336
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/15336
Therefore, the GCF of Fractions 1762/216,1858/284 is 2/15336
Least Common Multiple of 216,284 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 216,284 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(216,284) = 4
common factors(in case of two or more numbers have common factors) = 1
GCF(216,284) x common factors =4 x 1 = 4
LCM(216,284) = ( 216 × 284 ) / 4
LCM(216,284) = 61344 / 4
LCM(216,284) = 15336
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FAQs on GCF of Fractions of 1762/216, 1858/284
1. What is the HCF of 1762,1858?
The HCF of 1762,1858 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 1762/216, 1858/284?
Answer: GCF of Numerators as per given numbers 1762/216, 1858/284 is
GCF of Numerators i.e. for 1762,1858 is 2
LCM of denominators i.e. for 216,284 is 15336.
Thus, GCF of Fractions is 2/15336.Finally, GCF of Fractions for 1762/216, 1858/284 is 2/15336.