GCF of 97/414, 75/798, 370/567
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 97/414, 75/798, 370/567 i.e 1/495558 easily. The following is the detailed procedure to determine the greatest common factor of fractions 97/414, 75/798, 370/567.
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 97/414,75/798,370/567?
Given fractions are 97/414,75/798,370/567
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 97/414,75/798,370/567, numerators are 97,75,370
Denominators are 414,798,567
The GCF of 97,75,370 is 1 .
LCM of 414,798,567 is 495558.
The greatest common factor of 97/414,75/798,370/567 = [GCF of 97,75,370]/[LCM of 414,798,567]= 1/495558
Therefore, the GCF of 97/414,75/798,370/567 is 1/495558.
To find the highest common factor of 97,75,370, we have to find the factors of both numbers and list the highest common factor.
The factors of 97 are 1, 97
The factors of 75 are 1, 3, 5, 15, 25, 75
The factors of 370 are 1, 2, 5, 10, 37, 74, 185, 370
The HCF of 97,75,370 is 1.
Lets's calculate GCF of 97,75,370
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 97,75,370 By Matching Biggest Common Factor Method
Now, list down the factors of 97
:1,97
Now, list down the factors of 75
:1,3,5,15,25,75
Now, list down the factors of 370
:1,2,5,10,37,74,185,370
Greatest Common Factor
We found the factors 97,75,370 . The biggest common factor number is the GCF number.
So the greatest common factor 97,75,370 is 1.
Lets's calculate LCM of 414,798,567
| 2 | 414, 798, 567 |
| 3 | 207, 399, 567 |
| 3 | 69, 133, 189 |
| 7 | 23, 133, 63 |
| 23, 19, 9 |
∴ So the LCM of the given numbers is 2 x 3 x 3 x 7 x 23 x 19 x 9 = 495558
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/495558
Therefore, the GCF of Fractions 97/414,75/798,370/567 is 1/495558
Least Common Multiple of 414,798,567 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 414,798,567 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(414,798,567) = 3
common factors(in case of two or more numbers have common factors) = 126
GCF(414,798,567) x common factors =3 x 126 = 378
LCM(414,798,567) = ( 414 × 798 × 567 ) / 378
LCM(414,798,567) = 187320924 / 378
LCM(414,798,567) = 495558
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FAQs on GCF of Fractions of 97/414, 75/798, 370/567
1. What is the HCF of 97,75,370?
The HCF of 97,75,370 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 97/414, 75/798, 370/567?
Answer: GCF of Numerators as per given numbers 97/414, 75/798, 370/567 is
GCF of Numerators i.e. for 97,75,370 is 1
LCM of denominators i.e. for 414,798,567 is 495558.
Thus, GCF of Fractions is 1/495558.Finally, GCF of Fractions for 97/414, 75/798, 370/567 is 1/495558.