GCF of 1749/184, 4998/7106
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1749/184, 4998/7106 i.e 3/653752 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1749/184, 4998/7106.
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 1749/184,4998/7106?
Given fractions are 1749/184,4998/7106
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 1749/184,4998/7106, numerators are 1749,4998
Denominators are 184,7106
The GCF of 1749,4998 is 3 .
LCM of 184,7106 is 653752.
The greatest common factor of 1749/184,4998/7106 = [GCF of 1749,4998]/[LCM of 184,7106]= 3/653752
Therefore, the GCF of 1749/184,4998/7106 is 3/653752.
To find the highest common factor of 1749,4998, we have to find the factors of both numbers and list the highest common factor.
The factors of 1749 are 1, 3, 11, 33, 53, 159, 583, 1749
The factors of 4998 are 1, 2, 3, 6, 7, 14, 17, 21, 34, 42, 49, 51, 98, 102, 119, 147, 238, 294, 357, 714, 833, 1666, 2499, 4998
The HCF of 1749,4998 is 3.
Lets's calculate GCF of 1749,4998
| 3 | 1749, 4998 |
| 583, 1666 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 1749,4998 By Matching Biggest Common Factor Method
Now, list down the factors of 1749
:1,3,11,33,53,159,583,1749
Now, list down the factors of 4998
:1,2,3,6,7,14,17,21,34,42,49,51,98,102,119,147,238,294,357,714,833,1666,2499,4998
Greatest Common Factor
We found the factors 1749,4998 . The biggest common factor number is the GCF number.
So the greatest common factor 1749,4998 is 3.
Lets's calculate LCM of 184,7106
| 2 | 184, 7106 |
| 92, 3553 |
∴ So the LCM of the given numbers is 2 x 92 x 3553 = 653752
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/653752
Therefore, the GCF of Fractions 1749/184,4998/7106 is 3/653752
Least Common Multiple of 184,7106 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 184,7106 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(184,7106) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(184,7106) x common factors =2 x 1 = 2
LCM(184,7106) = ( 184 × 7106 ) / 2
LCM(184,7106) = 1307504 / 2
LCM(184,7106) = 653752
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FAQs on GCF of Fractions of 1749/184, 4998/7106
1. What is the HCF of 1749,4998?
The HCF of 1749,4998 is 3
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 1749/184, 4998/7106?
Answer: GCF of Numerators as per given numbers 1749/184, 4998/7106 is
GCF of Numerators i.e. for 1749,4998 is 3
LCM of denominators i.e. for 184,7106 is 653752.
Thus, GCF of Fractions is 3/653752.Finally, GCF of Fractions for 1749/184, 4998/7106 is 3/653752.