GCF of 34/74, 69/40, 14/25, 22/30
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 34/74, 69/40, 14/25, 22/30 i.e 1/22200 easily. The following is the detailed procedure to determine the greatest common factor of fractions 34/74, 69/40, 14/25, 22/30.
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 34/74,69/40,14/25,22/30?
Given fractions are 34/74,69/40,14/25,22/30
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 34/74,69/40,14/25,22/30, numerators are 34,69,14,22
Denominators are 74,40,25,30
The GCF of 34,69,14,22 is 1 .
LCM of 74,40,25,30 is 22200.
The greatest common factor of 34/74,69/40,14/25,22/30 = [GCF of 34,69,14,22]/[LCM of 74,40,25,30]= 1/22200
Therefore, the GCF of 34/74,69/40,14/25,22/30 is 1/22200.
To find the highest common factor of 34,69,14,22, we have to find the factors of both numbers and list the highest common factor.
The factors of 34 are 1, 2, 17, 34
The factors of 69 are 1, 3, 23, 69
The factors of 14 are 1, 2, 7, 14
The factors of 22 are 1, 2, 11, 22
The HCF of 34,69,14,22 is 1.
Lets's calculate GCF of 34,69,14,22
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 34,69,14,22 By Matching Biggest Common Factor Method
Now, list down the factors of 34
:1,2,17,34
Now, list down the factors of 69
:1,3,23,69
Now, list down the factors of 14
:1,2,7,14
Now, list down the factors of 22
:1,2,11,22
Greatest Common Factor
We found the factors 34,69,14,22 . The biggest common factor number is the GCF number.
So the greatest common factor 34,69,14,22 is 1.
Lets's calculate LCM of 74,40,25,30
| 2 | 74, 40, 25, 30 |
| 5 | 37, 20, 25, 15 |
| 37, 4, 5, 3 |
∴ So the LCM of the given numbers is 2 x 5 x 37 x 4 x 5 x 3 = 22200
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/22200
Therefore, the GCF of Fractions 34/74,69/40,14/25,22/30 is 1/22200
Least Common Multiple of 74,40,25,30 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 74,40,25,30 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(74,40,25,30) = 1
common factors(in case of two or more numbers have common factors) = 100
GCF(74,40,25,30) x common factors =1 x 100 = 100
LCM(74,40,25,30) = ( 74 × 40 × 25 × 30 ) / 100
LCM(74,40,25,30) = 2220000 / 100
LCM(74,40,25,30) = 22200
GCF of Fractions Calculation Examples
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FAQs on GCF of Fractions of 34/74, 69/40, 14/25, 22/30
1. What is the HCF of 34,69,14,22?
The HCF of 34,69,14,22 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 34/74, 69/40, 14/25, 22/30?
Answer: GCF of Numerators as per given numbers 34/74, 69/40, 14/25, 22/30 is
GCF of Numerators i.e. for 34,69,14,22 is 1
LCM of denominators i.e. for 74,40,25,30 is 22200.
Thus, GCF of Fractions is 1/22200.Finally, GCF of Fractions for 34/74, 69/40, 14/25, 22/30 is 1/22200.