GCF of 7314/984, 8930/8144
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 7314/984, 8930/8144 i.e 2/1001712 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7314/984, 8930/8144.
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 7314/984,8930/8144?
Given fractions are 7314/984,8930/8144
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 7314/984,8930/8144, numerators are 7314,8930
Denominators are 984,8144
The GCF of 7314,8930 is 2 .
LCM of 984,8144 is 1001712.
The greatest common factor of 7314/984,8930/8144 = [GCF of 7314,8930]/[LCM of 984,8144]= 2/1001712
Therefore, the GCF of 7314/984,8930/8144 is 2/1001712.
To find the highest common factor of 7314,8930, we have to find the factors of both numbers and list the highest common factor.
The factors of 7314 are 1, 2, 3, 6, 23, 46, 53, 69, 106, 138, 159, 318, 1219, 2438, 3657, 7314
The factors of 8930 are 1, 2, 5, 10, 19, 38, 47, 94, 95, 190, 235, 470, 893, 1786, 4465, 8930
The HCF of 7314,8930 is 2.
Lets's calculate GCF of 7314,8930
| 2 | 7314, 8930 |
| 3657, 4465 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 7314,8930 By Matching Biggest Common Factor Method
Now, list down the factors of 7314
:1,2,3,6,23,46,53,69,106,138,159,318,1219,2438,3657,7314
Now, list down the factors of 8930
:1,2,5,10,19,38,47,94,95,190,235,470,893,1786,4465,8930
Greatest Common Factor
We found the factors 7314,8930 . The biggest common factor number is the GCF number.
So the greatest common factor 7314,8930 is 2.
Lets's calculate LCM of 984,8144
| 2 | 984, 8144 |
| 2 | 492, 4072 |
| 2 | 246, 2036 |
| 123, 1018 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 123 x 1018 = 1001712
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/1001712
Therefore, the GCF of Fractions 7314/984,8930/8144 is 2/1001712
Least Common Multiple of 984,8144 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 984,8144 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(984,8144) = 8
common factors(in case of two or more numbers have common factors) = 1
GCF(984,8144) x common factors =8 x 1 = 8
LCM(984,8144) = ( 984 × 8144 ) / 8
LCM(984,8144) = 8013696 / 8
LCM(984,8144) = 1001712
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 7314/984, 8930/8144
1. What is the HCF of 7314,8930?
The HCF of 7314,8930 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 7314/984, 8930/8144?
Answer: GCF of Numerators as per given numbers 7314/984, 8930/8144 is
GCF of Numerators i.e. for 7314,8930 is 2
LCM of denominators i.e. for 984,8144 is 1001712.
Thus, GCF of Fractions is 2/1001712.Finally, GCF of Fractions for 7314/984, 8930/8144 is 2/1001712.