GCF of 51/74, 990/88, 312/978
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 51/74, 990/88, 312/978 i.e 3/1592184 easily. The following is the detailed procedure to determine the greatest common factor of fractions 51/74, 990/88, 312/978.
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 51/74,990/88,312/978?
Given fractions are 51/74,990/88,312/978
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 51/74,990/88,312/978, numerators are 51,990,312
Denominators are 74,88,978
The GCF of 51,990,312 is 3 .
LCM of 74,88,978 is 1592184.
The greatest common factor of 51/74,990/88,312/978 = [GCF of 51,990,312]/[LCM of 74,88,978]= 3/1592184
Therefore, the GCF of 51/74,990/88,312/978 is 3/1592184.
To find the highest common factor of 51,990,312, we have to find the factors of both numbers and list the highest common factor.
The factors of 51 are 1, 3, 17, 51
The factors of 990 are 1, 2, 3, 5, 6, 9, 10, 11, 15, 18, 22, 30, 33, 45, 55, 66, 90, 99, 110, 165, 198, 330, 495, 990
The factors of 312 are 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, 312
The HCF of 51,990,312 is 3.
Lets's calculate GCF of 51,990,312
| 3 | 51, 990, 312 |
| 17, 330, 104 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 51,990,312 By Matching Biggest Common Factor Method
Now, list down the factors of 51
:1,3,17,51
Now, list down the factors of 990
:1,2,3,5,6,9,10,11,15,18,22,30,33,45,55,66,90,99,110,165,198,330,495,990
Now, list down the factors of 312
:1,2,3,4,6,8,12,13,24,26,39,52,78,104,156,312
Greatest Common Factor
We found the factors 51,990,312 . The biggest common factor number is the GCF number.
So the greatest common factor 51,990,312 is 3.
Lets's calculate LCM of 74,88,978
| 2 | 74, 88, 978 |
| 37, 44, 489 |
∴ So the LCM of the given numbers is 2 x 37 x 44 x 489 = 1592184
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/1592184
Therefore, the GCF of Fractions 51/74,990/88,312/978 is 3/1592184
Least Common Multiple of 74,88,978 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 74,88,978 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(74,88,978) = 2
common factors(in case of two or more numbers have common factors) = 2
GCF(74,88,978) x common factors =2 x 2 = 4
LCM(74,88,978) = ( 74 × 88 × 978 ) / 4
LCM(74,88,978) = 6368736 / 4
LCM(74,88,978) = 1592184
GCF of Fractions Calculation Examples
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FAQs on GCF of Fractions of 51/74, 990/88, 312/978
1. What is the HCF of 51,990,312?
The HCF of 51,990,312 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 51/74, 990/88, 312/978?
Answer: GCF of Numerators as per given numbers 51/74, 990/88, 312/978 is
GCF of Numerators i.e. for 51,990,312 is 3
LCM of denominators i.e. for 74,88,978 is 1592184.
Thus, GCF of Fractions is 3/1592184.Finally, GCF of Fractions for 51/74, 990/88, 312/978 is 3/1592184.