GCF of 30/40, 75/20, 119/700
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 30/40, 75/20, 119/700 i.e 1/1400 easily. The following is the detailed procedure to determine the greatest common factor of fractions 30/40, 75/20, 119/700.
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 30/40,75/20,119/700?
Given fractions are 30/40,75/20,119/700
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 30/40,75/20,119/700, numerators are 30,75,119
Denominators are 40,20,700
The GCF of 30,75,119 is 1 .
LCM of 40,20,700 is 1400.
The greatest common factor of 30/40,75/20,119/700 = [GCF of 30,75,119]/[LCM of 40,20,700]= 1/1400
Therefore, the GCF of 30/40,75/20,119/700 is 1/1400.
To find the highest common factor of 30,75,119, we have to find the factors of both numbers and list the highest common factor.
The factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30
The factors of 75 are 1, 3, 5, 15, 25, 75
The factors of 119 are 1, 7, 17, 119
The HCF of 30,75,119 is 1.
Lets's calculate GCF of 30,75,119
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 30,75,119 By Matching Biggest Common Factor Method
Now, list down the factors of 30
:1,2,3,5,6,10,15,30
Now, list down the factors of 75
:1,3,5,15,25,75
Now, list down the factors of 119
:1,7,17,119
Greatest Common Factor
We found the factors 30,75,119 . The biggest common factor number is the GCF number.
So the greatest common factor 30,75,119 is 1.
Lets's calculate LCM of 40,20,700
| 2 | 40, 20, 700 |
| 2 | 20, 10, 350 |
| 5 | 5, 10, 175 |
| 1, 2, 35 |
∴ So the LCM of the given numbers is 2 x 2 x 5 x 1 x 2 x 35 = 1400
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/1400
Therefore, the GCF of Fractions 30/40,75/20,119/700 is 1/1400
Least Common Multiple of 40,20,700 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 40,20,700 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(40,20,700) = 20
common factors(in case of two or more numbers have common factors) = 20
GCF(40,20,700) x common factors =20 x 20 = 400
LCM(40,20,700) = ( 40 × 20 × 700 ) / 400
LCM(40,20,700) = 560000 / 400
LCM(40,20,700) = 1400
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FAQs on GCF of Fractions of 30/40, 75/20, 119/700
1. What is the HCF of 30,75,119?
The HCF of 30,75,119 is 1
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 30/40, 75/20, 119/700?
Answer: GCF of Numerators as per given numbers 30/40, 75/20, 119/700 is
GCF of Numerators i.e. for 30,75,119 is 1
LCM of denominators i.e. for 40,20,700 is 1400.
Thus, GCF of Fractions is 1/1400.Finally, GCF of Fractions for 30/40, 75/20, 119/700 is 1/1400.