GCF of 1974/82, 6486/689
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1974/82, 6486/689 i.e 282/56498 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1974/82, 6486/689.
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 1974/82,6486/689?
Given fractions are 1974/82,6486/689
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 1974/82,6486/689, numerators are 1974,6486
Denominators are 82,689
The GCF of 1974,6486 is 282 .
LCM of 82,689 is 56498.
The greatest common factor of 1974/82,6486/689 = [GCF of 1974,6486]/[LCM of 82,689]= 282/56498
Therefore, the GCF of 1974/82,6486/689 is 282/56498.
To find the highest common factor of 1974,6486, 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 6486 are 1, 2, 3, 6, 23, 46, 47, 69, 94, 138, 141, 282, 1081, 2162, 3243, 6486
The HCF of 1974,6486 is 282.
Lets's calculate GCF of 1974,6486
| 2 | 1974, 6486 |
| 3 | 987, 3243 |
| 47 | 329, 1081 |
| 7, 23 |
∴ So the GCF of the given numbers is 2 x 3 x 47 = 282
Greatest Common Factor of 1974,6486 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 6486
:1,2,3,6,23,46,47,69,94,138,141,282,1081,2162,3243,6486
Greatest Common Factor
We found the factors 1974,6486 . The biggest common factor number is the GCF number.
So the greatest common factor 1974,6486 is 282.
Lets's calculate LCM of 82,689
Given numbers has no common factors except 1. So, there LCM is their product i.e 56498
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 282/56498
Therefore, the GCF of Fractions 1974/82,6486/689 is 282/56498
Least Common Multiple of 82,689 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 82,689 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(82,689) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(82,689) x common factors =1 x 1 = 1
LCM(82,689) = ( 82 × 689 ) / 1
LCM(82,689) = 56498 / 1
LCM(82,689) = 56498
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FAQs on GCF of Fractions of 1974/82, 6486/689
1. What is the HCF of 1974,6486?
The HCF of 1974,6486 is 282
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 1974/82, 6486/689?
Answer: GCF of Numerators as per given numbers 1974/82, 6486/689 is
GCF of Numerators i.e. for 1974,6486 is 282
LCM of denominators i.e. for 82,689 is 56498.
Thus, GCF of Fractions is 282/56498.Finally, GCF of Fractions for 1974/82, 6486/689 is 282/56498.