GCF of 63/31, 90/45, 74/90, 29/65
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 63/31, 90/45, 74/90, 29/65 i.e 1/36270 easily. The following is the detailed procedure to determine the greatest common factor of fractions 63/31, 90/45, 74/90, 29/65.
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 63/31,90/45,74/90,29/65?
Given fractions are 63/31,90/45,74/90,29/65
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 63/31,90/45,74/90,29/65, numerators are 63,90,74,29
Denominators are 31,45,90,65
The GCF of 63,90,74,29 is 1 .
LCM of 31,45,90,65 is 36270.
The greatest common factor of 63/31,90/45,74/90,29/65 = [GCF of 63,90,74,29]/[LCM of 31,45,90,65]= 1/36270
Therefore, the GCF of 63/31,90/45,74/90,29/65 is 1/36270.
To find the highest common factor of 63,90,74,29, we have to find the factors of both numbers and list the highest common factor.
The factors of 63 are 1, 3, 7, 9, 21, 63
The factors of 90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90
The factors of 74 are 1, 2, 37, 74
The factors of 29 are 1, 29
The HCF of 63,90,74,29 is 1.
Lets's calculate GCF of 63,90,74,29
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 63,90,74,29 By Matching Biggest Common Factor Method
Now, list down the factors of 63
:1,3,7,9,21,63
Now, list down the factors of 90
:1,2,3,5,6,9,10,15,18,30,45,90
Now, list down the factors of 74
:1,2,37,74
Now, list down the factors of 29
:1,29
Greatest Common Factor
We found the factors 63,90,74,29 . The biggest common factor number is the GCF number.
So the greatest common factor 63,90,74,29 is 1.
Lets's calculate LCM of 31,45,90,65
| 3 | 31, 45, 90, 65 |
| 3 | 31, 15, 30, 65 |
| 5 | 31, 5, 10, 65 |
| 31, 1, 2, 13 |
∴ So the LCM of the given numbers is 3 x 3 x 5 x 31 x 1 x 2 x 13 = 36270
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/36270
Therefore, the GCF of Fractions 63/31,90/45,74/90,29/65 is 1/36270
Least Common Multiple of 31,45,90,65 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 31,45,90,65 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(31,45,90,65) = 1
common factors(in case of two or more numbers have common factors) = 225
GCF(31,45,90,65) x common factors =1 x 225 = 225
LCM(31,45,90,65) = ( 31 × 45 × 90 × 65 ) / 225
LCM(31,45,90,65) = 8160750 / 225
LCM(31,45,90,65) = 36270
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 63/31, 90/45, 74/90, 29/65
1. What is the HCF of 63,90,74,29?
The HCF of 63,90,74,29 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 63/31, 90/45, 74/90, 29/65?
Answer: GCF of Numerators as per given numbers 63/31, 90/45, 74/90, 29/65 is
GCF of Numerators i.e. for 63,90,74,29 is 1
LCM of denominators i.e. for 31,45,90,65 is 36270.
Thus, GCF of Fractions is 1/36270.Finally, GCF of Fractions for 63/31, 90/45, 74/90, 29/65 is 1/36270.