GCF of 6/75, 72/28, 32/495, 245/749
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 6/75, 72/28, 32/495, 245/749 i.e 1/7415100 easily. The following is the detailed procedure to determine the greatest common factor of fractions 6/75, 72/28, 32/495, 245/749.
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 6/75,72/28,32/495,245/749?
Given fractions are 6/75,72/28,32/495,245/749
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 6/75,72/28,32/495,245/749, numerators are 6,72,32,245
Denominators are 75,28,495,749
The GCF of 6,72,32,245 is 1 .
LCM of 75,28,495,749 is 7415100.
The greatest common factor of 6/75,72/28,32/495,245/749 = [GCF of 6,72,32,245]/[LCM of 75,28,495,749]= 1/7415100
Therefore, the GCF of 6/75,72/28,32/495,245/749 is 1/7415100.
To find the highest common factor of 6,72,32,245, we have to find the factors of both numbers and list the highest common factor.
The factors of 6 are 1, 2, 3, 6
The factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
The factors of 32 are 1, 2, 4, 8, 16, 32
The factors of 245 are 1, 5, 7, 35, 49, 245
The HCF of 6,72,32,245 is 1.
Lets's calculate GCF of 6,72,32,245
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 6,72,32,245 By Matching Biggest Common Factor Method
Now, list down the factors of 6
:1,2,3,6
Now, list down the factors of 72
:1,2,3,4,6,8,9,12,18,24,36,72
Now, list down the factors of 32
:1,2,4,8,16,32
Now, list down the factors of 245
:1,5,7,35,49,245
Greatest Common Factor
We found the factors 6,72,32,245 . The biggest common factor number is the GCF number.
So the greatest common factor 6,72,32,245 is 1.
Lets's calculate LCM of 75,28,495,749
| 3 | 75, 28, 495, 749 |
| 5 | 25, 28, 165, 749 |
| 7 | 5, 28, 33, 749 |
| 5, 4, 33, 107 |
∴ So the LCM of the given numbers is 3 x 5 x 7 x 5 x 4 x 33 x 107 = 7415100
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/7415100
Therefore, the GCF of Fractions 6/75,72/28,32/495,245/749 is 1/7415100
Least Common Multiple of 75,28,495,749 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 75,28,495,749 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(75,28,495,749) = 1
common factors(in case of two or more numbers have common factors) = 105
GCF(75,28,495,749) x common factors =1 x 105 = 105
LCM(75,28,495,749) = ( 75 × 28 × 495 × 749 ) / 105
LCM(75,28,495,749) = 778585500 / 105
LCM(75,28,495,749) = 7415100
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 6/75, 72/28, 32/495, 245/749
1. What is the HCF of 6,72,32,245?
The HCF of 6,72,32,245 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 6/75, 72/28, 32/495, 245/749?
Answer: GCF of Numerators as per given numbers 6/75, 72/28, 32/495, 245/749 is
GCF of Numerators i.e. for 6,72,32,245 is 1
LCM of denominators i.e. for 75,28,495,749 is 7415100.
Thus, GCF of Fractions is 1/7415100.Finally, GCF of Fractions for 6/75, 72/28, 32/495, 245/749 is 1/7415100.