GCF of 12/69, 63/23, 40/30, 67/66
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 12/69, 63/23, 40/30, 67/66 i.e 1/7590 easily. The following is the detailed procedure to determine the greatest common factor of fractions 12/69, 63/23, 40/30, 67/66.
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 12/69,63/23,40/30,67/66?
Given fractions are 12/69,63/23,40/30,67/66
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 12/69,63/23,40/30,67/66, numerators are 12,63,40,67
Denominators are 69,23,30,66
The GCF of 12,63,40,67 is 1 .
LCM of 69,23,30,66 is 7590.
The greatest common factor of 12/69,63/23,40/30,67/66 = [GCF of 12,63,40,67]/[LCM of 69,23,30,66]= 1/7590
Therefore, the GCF of 12/69,63/23,40/30,67/66 is 1/7590.
To find the highest common factor of 12,63,40,67, we have to find the factors of both numbers and list the highest common factor.
The factors of 12 are 1, 2, 3, 4, 6, 12
The factors of 63 are 1, 3, 7, 9, 21, 63
The factors of 40 are 1, 2, 4, 5, 8, 10, 20, 40
The factors of 67 are 1, 67
The HCF of 12,63,40,67 is 1.
Lets's calculate GCF of 12,63,40,67
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 12,63,40,67 By Matching Biggest Common Factor Method
Now, list down the factors of 12
:1,2,3,4,6,12
Now, list down the factors of 63
:1,3,7,9,21,63
Now, list down the factors of 40
:1,2,4,5,8,10,20,40
Now, list down the factors of 67
:1,67
Greatest Common Factor
We found the factors 12,63,40,67 . The biggest common factor number is the GCF number.
So the greatest common factor 12,63,40,67 is 1.
Lets's calculate LCM of 69,23,30,66
| 2 | 69, 23, 30, 66 |
| 3 | 69, 23, 15, 33 |
| 23 | 23, 23, 5, 11 |
| 1, 1, 5, 11 |
∴ So the LCM of the given numbers is 2 x 3 x 23 x 1 x 1 x 5 x 11 = 7590
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/7590
Therefore, the GCF of Fractions 12/69,63/23,40/30,67/66 is 1/7590
Least Common Multiple of 69,23,30,66 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 69,23,30,66 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(69,23,30,66) = 1
common factors(in case of two or more numbers have common factors) = 414
GCF(69,23,30,66) x common factors =1 x 414 = 414
LCM(69,23,30,66) = ( 69 × 23 × 30 × 66 ) / 414
LCM(69,23,30,66) = 3142260 / 414
LCM(69,23,30,66) = 7590
GCF of Fractions Calculation Examples
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FAQs on GCF of Fractions of 12/69, 63/23, 40/30, 67/66
1. What is the HCF of 12,63,40,67?
The HCF of 12,63,40,67 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 12/69, 63/23, 40/30, 67/66?
Answer: GCF of Numerators as per given numbers 12/69, 63/23, 40/30, 67/66 is
GCF of Numerators i.e. for 12,63,40,67 is 1
LCM of denominators i.e. for 69,23,30,66 is 7590.
Thus, GCF of Fractions is 1/7590.Finally, GCF of Fractions for 12/69, 63/23, 40/30, 67/66 is 1/7590.