GCF of 1578/646, 9778/1717
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1578/646, 9778/1717 i.e 2/65246 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1578/646, 9778/1717.
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 1578/646,9778/1717?
Given fractions are 1578/646,9778/1717
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 1578/646,9778/1717, numerators are 1578,9778
Denominators are 646,1717
The GCF of 1578,9778 is 2 .
LCM of 646,1717 is 65246.
The greatest common factor of 1578/646,9778/1717 = [GCF of 1578,9778]/[LCM of 646,1717]= 2/65246
Therefore, the GCF of 1578/646,9778/1717 is 2/65246.
To find the highest common factor of 1578,9778, we have to find the factors of both numbers and list the highest common factor.
The factors of 1578 are 1, 2, 3, 6, 263, 526, 789, 1578
The factors of 9778 are 1, 2, 4889, 9778
The HCF of 1578,9778 is 2.
Lets's calculate GCF of 1578,9778
| 2 | 1578, 9778 |
| 789, 4889 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 1578,9778 By Matching Biggest Common Factor Method
Now, list down the factors of 1578
:1,2,3,6,263,526,789,1578
Now, list down the factors of 9778
:1,2,4889,9778
Greatest Common Factor
We found the factors 1578,9778 . The biggest common factor number is the GCF number.
So the greatest common factor 1578,9778 is 2.
Lets's calculate LCM of 646,1717
| 17 | 646, 1717 |
| 38, 101 |
∴ So the LCM of the given numbers is 17 x 38 x 101 = 65246
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/65246
Therefore, the GCF of Fractions 1578/646,9778/1717 is 2/65246
Least Common Multiple of 646,1717 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 646,1717 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(646,1717) = 17
common factors(in case of two or more numbers have common factors) = 1
GCF(646,1717) x common factors =17 x 1 = 17
LCM(646,1717) = ( 646 × 1717 ) / 17
LCM(646,1717) = 1109182 / 17
LCM(646,1717) = 65246
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FAQs on GCF of Fractions of 1578/646, 9778/1717
1. What is the HCF of 1578,9778?
The HCF of 1578,9778 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 1578/646, 9778/1717?
Answer: GCF of Numerators as per given numbers 1578/646, 9778/1717 is
GCF of Numerators i.e. for 1578,9778 is 2
LCM of denominators i.e. for 646,1717 is 65246.
Thus, GCF of Fractions is 2/65246.Finally, GCF of Fractions for 1578/646, 9778/1717 is 2/65246.