GCF of 18/34, 12/120, 735/700
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 18/34, 12/120, 735/700 i.e 3/71400 easily. The following is the detailed procedure to determine the greatest common factor of fractions 18/34, 12/120, 735/700.
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 18/34,12/120,735/700?
Given fractions are 18/34,12/120,735/700
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 18/34,12/120,735/700, numerators are 18,12,735
Denominators are 34,120,700
The GCF of 18,12,735 is 3 .
LCM of 34,120,700 is 71400.
The greatest common factor of 18/34,12/120,735/700 = [GCF of 18,12,735]/[LCM of 34,120,700]= 3/71400
Therefore, the GCF of 18/34,12/120,735/700 is 3/71400.
To find the highest common factor of 18,12,735, we have to find the factors of both numbers and list the highest common factor.
The factors of 18 are 1, 2, 3, 6, 9, 18
The factors of 12 are 1, 2, 3, 4, 6, 12
The factors of 735 are 1, 3, 5, 7, 15, 21, 35, 49, 105, 147, 245, 735
The HCF of 18,12,735 is 3.
Lets's calculate GCF of 18,12,735
| 3 | 18, 12, 735 |
| 6, 4, 245 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 18,12,735 By Matching Biggest Common Factor Method
Now, list down the factors of 18
:1,2,3,6,9,18
Now, list down the factors of 12
:1,2,3,4,6,12
Now, list down the factors of 735
:1,3,5,7,15,21,35,49,105,147,245,735
Greatest Common Factor
We found the factors 18,12,735 . The biggest common factor number is the GCF number.
So the greatest common factor 18,12,735 is 3.
Lets's calculate LCM of 34,120,700
| 2 | 34, 120, 700 |
| 2 | 17, 60, 350 |
| 5 | 17, 30, 175 |
| 17, 6, 35 |
∴ So the LCM of the given numbers is 2 x 2 x 5 x 17 x 6 x 35 = 71400
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/71400
Therefore, the GCF of Fractions 18/34,12/120,735/700 is 3/71400
Least Common Multiple of 34,120,700 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 34,120,700 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(34,120,700) = 2
common factors(in case of two or more numbers have common factors) = 20
GCF(34,120,700) x common factors =2 x 20 = 40
LCM(34,120,700) = ( 34 × 120 × 700 ) / 40
LCM(34,120,700) = 2856000 / 40
LCM(34,120,700) = 71400
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FAQs on GCF of Fractions of 18/34, 12/120, 735/700
1. What is the HCF of 18,12,735?
The HCF of 18,12,735 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 18/34, 12/120, 735/700?
Answer: GCF of Numerators as per given numbers 18/34, 12/120, 735/700 is
GCF of Numerators i.e. for 18,12,735 is 3
LCM of denominators i.e. for 34,120,700 is 71400.
Thus, GCF of Fractions is 3/71400.Finally, GCF of Fractions for 18/34, 12/120, 735/700 is 3/71400.