GCF of 120/213, 7350/749
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 120/213, 7350/749 i.e 30/159537 easily. The following is the detailed procedure to determine the greatest common factor of fractions 120/213, 7350/749.
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 120/213,7350/749?
Given fractions are 120/213,7350/749
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 120/213,7350/749, numerators are 120,7350
Denominators are 213,749
The GCF of 120,7350 is 30 .
LCM of 213,749 is 159537.
The greatest common factor of 120/213,7350/749 = [GCF of 120,7350]/[LCM of 213,749]= 30/159537
Therefore, the GCF of 120/213,7350/749 is 30/159537.
To find the highest common factor of 120,7350, we have to find the factors of both numbers and list the highest common factor.
The factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
The factors of 7350 are 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 25, 30, 35, 42, 49, 50, 70, 75, 98, 105, 147, 150, 175, 210, 245, 294, 350, 490, 525, 735, 1050, 1225, 1470, 2450, 3675, 7350
The HCF of 120,7350 is 30.
Lets's calculate GCF of 120,7350
| 2 | 120, 7350 |
| 3 | 60, 3675 |
| 5 | 20, 1225 |
| 4, 245 |
∴ So the GCF of the given numbers is 2 x 3 x 5 = 30
Greatest Common Factor of 120,7350 By Matching Biggest Common Factor Method
Now, list down the factors of 120
:1,2,3,4,5,6,8,10,12,15,20,24,30,40,60,120
Now, list down the factors of 7350
:1,2,3,5,6,7,10,14,15,21,25,30,35,42,49,50,70,75,98,105,147,150,175,210,245,294,350,490,525,735,1050,1225,1470,2450,3675,7350
Greatest Common Factor
We found the factors 120,7350 . The biggest common factor number is the GCF number.
So the greatest common factor 120,7350 is 30.
Lets's calculate LCM of 213,749
Given numbers has no common factors except 1. So, there LCM is their product i.e 159537
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 30/159537
Therefore, the GCF of Fractions 120/213,7350/749 is 30/159537
Least Common Multiple of 213,749 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 213,749 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(213,749) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(213,749) x common factors =1 x 1 = 1
LCM(213,749) = ( 213 × 749 ) / 1
LCM(213,749) = 159537 / 1
LCM(213,749) = 159537
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FAQs on GCF of Fractions of 120/213, 7350/749
1. What is the HCF of 120,7350?
The HCF of 120,7350 is 30
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 120/213, 7350/749?
Answer: GCF of Numerators as per given numbers 120/213, 7350/749 is
GCF of Numerators i.e. for 120,7350 is 30
LCM of denominators i.e. for 213,749 is 159537.
Thus, GCF of Fractions is 30/159537.Finally, GCF of Fractions for 120/213, 7350/749 is 30/159537.