GCF of 1974/751, 1953/3514
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1974/751, 1953/3514 i.e 21/2639014 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1974/751, 1953/3514.
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 1974/751,1953/3514?
Given fractions are 1974/751,1953/3514
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 1974/751,1953/3514, numerators are 1974,1953
Denominators are 751,3514
The GCF of 1974,1953 is 21 .
LCM of 751,3514 is 2639014.
The greatest common factor of 1974/751,1953/3514 = [GCF of 1974,1953]/[LCM of 751,3514]= 21/2639014
Therefore, the GCF of 1974/751,1953/3514 is 21/2639014.
To find the highest common factor of 1974,1953, we have to find the factors of both numbers and list the highest common factor.
The factors of 1974 are 1, 2, 3, 6, 7, 14, 21, 42, 47, 94, 141, 282, 329, 658, 987, 1974
The factors of 1953 are 1, 3, 7, 9, 21, 31, 63, 93, 217, 279, 651, 1953
The HCF of 1974,1953 is 21.
Lets's calculate GCF of 1974,1953
| 3 | 1974, 1953 |
| 7 | 658, 651 |
| 94, 93 |
∴ So the GCF of the given numbers is 3 x 7 = 21
Greatest Common Factor of 1974,1953 By Matching Biggest Common Factor Method
Now, list down the factors of 1974
:1,2,3,6,7,14,21,42,47,94,141,282,329,658,987,1974
Now, list down the factors of 1953
:1,3,7,9,21,31,63,93,217,279,651,1953
Greatest Common Factor
We found the factors 1974,1953 . The biggest common factor number is the GCF number.
So the greatest common factor 1974,1953 is 21.
Lets's calculate LCM of 751,3514
Given numbers has no common factors except 1. So, there LCM is their product i.e 2639014
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 21/2639014
Therefore, the GCF of Fractions 1974/751,1953/3514 is 21/2639014
Least Common Multiple of 751,3514 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 751,3514 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(751,3514) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(751,3514) x common factors =1 x 1 = 1
LCM(751,3514) = ( 751 × 3514 ) / 1
LCM(751,3514) = 2639014 / 1
LCM(751,3514) = 2639014
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FAQs on GCF of Fractions of 1974/751, 1953/3514
1. What is the HCF of 1974,1953?
The HCF of 1974,1953 is 21
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 1974/751, 1953/3514?
Answer: GCF of Numerators as per given numbers 1974/751, 1953/3514 is
GCF of Numerators i.e. for 1974,1953 is 21
LCM of denominators i.e. for 751,3514 is 2639014.
Thus, GCF of Fractions is 21/2639014.Finally, GCF of Fractions for 1974/751, 1953/3514 is 21/2639014.