GCF of 600/974, 240/274
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 600/974, 240/274 i.e 120/133438 easily. The following is the detailed procedure to determine the greatest common factor of fractions 600/974, 240/274.
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 600/974,240/274?
Given fractions are 600/974,240/274
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 600/974,240/274, numerators are 600,240
Denominators are 974,274
The GCF of 600,240 is 120 .
LCM of 974,274 is 133438.
The greatest common factor of 600/974,240/274 = [GCF of 600,240]/[LCM of 974,274]= 120/133438
Therefore, the GCF of 600/974,240/274 is 120/133438.
To find the highest common factor of 600,240, we have to find the factors of both numbers and list the highest common factor.
The factors of 600 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 25, 30, 40, 50, 60, 75, 100, 120, 150, 200, 300, 600
The factors of 240 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 240
The HCF of 600,240 is 120.
Lets's calculate GCF of 600,240
| 2 | 600, 240 |
| 2 | 300, 120 |
| 2 | 150, 60 |
| 3 | 75, 30 |
| 5 | 25, 10 |
| 5, 2 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 3 x 5 = 120
Greatest Common Factor of 600,240 By Matching Biggest Common Factor Method
Now, list down the factors of 600
:1,2,3,4,5,6,8,10,12,15,20,24,25,30,40,50,60,75,100,120,150,200,300,600
Now, list down the factors of 240
:1,2,3,4,5,6,8,10,12,15,16,20,24,30,40,48,60,80,120,240
Greatest Common Factor
We found the factors 600,240 . The biggest common factor number is the GCF number.
So the greatest common factor 600,240 is 120.
Lets's calculate LCM of 974,274
| 2 | 974, 274 |
| 487, 137 |
∴ So the LCM of the given numbers is 2 x 487 x 137 = 133438
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 120/133438
Therefore, the GCF of Fractions 600/974,240/274 is 120/133438
Least Common Multiple of 974,274 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 974,274 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(974,274) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(974,274) x common factors =2 x 1 = 2
LCM(974,274) = ( 974 × 274 ) / 2
LCM(974,274) = 266876 / 2
LCM(974,274) = 133438
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FAQs on GCF of Fractions of 600/974, 240/274
1. What is the HCF of 600,240?
The HCF of 600,240 is 120
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 600/974, 240/274?
Answer: GCF of Numerators as per given numbers 600/974, 240/274 is
GCF of Numerators i.e. for 600,240 is 120
LCM of denominators i.e. for 974,274 is 133438.
Thus, GCF of Fractions is 120/133438.Finally, GCF of Fractions for 600/974, 240/274 is 120/133438.