GCF of 8417/598, 9720/403
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 8417/598, 9720/403 i.e 1/18538 easily. The following is the detailed procedure to determine the greatest common factor of fractions 8417/598, 9720/403.
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 8417/598,9720/403?
Given fractions are 8417/598,9720/403
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 8417/598,9720/403, numerators are 8417,9720
Denominators are 598,403
The GCF of 8417,9720 is 1 .
LCM of 598,403 is 18538.
The greatest common factor of 8417/598,9720/403 = [GCF of 8417,9720]/[LCM of 598,403]= 1/18538
Therefore, the GCF of 8417/598,9720/403 is 1/18538.
To find the highest common factor of 8417,9720, we have to find the factors of both numbers and list the highest common factor.
The factors of 8417 are 1, 19, 443, 8417
The factors of 9720 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 27, 30, 36, 40, 45, 54, 60, 72, 81, 90, 108, 120, 135, 162, 180, 216, 243, 270, 324, 360, 405, 486, 540, 648, 810, 972, 1080, 1215, 1620, 1944, 2430, 3240, 4860, 9720
The HCF of 8417,9720 is 1.
Lets's calculate GCF of 8417,9720
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 8417,9720 By Matching Biggest Common Factor Method
Now, list down the factors of 8417
:1,19,443,8417
Now, list down the factors of 9720
:1,2,3,4,5,6,8,9,10,12,15,18,20,24,27,30,36,40,45,54,60,72,81,90,108,120,135,162,180,216,243,270,324,360,405,486,540,648,810,972,1080,1215,1620,1944,2430,3240,4860,9720
Greatest Common Factor
We found the factors 8417,9720 . The biggest common factor number is the GCF number.
So the greatest common factor 8417,9720 is 1.
Lets's calculate LCM of 598,403
| 13 | 598, 403 |
| 46, 31 |
∴ So the LCM of the given numbers is 13 x 46 x 31 = 18538
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/18538
Therefore, the GCF of Fractions 8417/598,9720/403 is 1/18538
Least Common Multiple of 598,403 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 598,403 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(598,403) = 13
common factors(in case of two or more numbers have common factors) = 1
GCF(598,403) x common factors =13 x 1 = 13
LCM(598,403) = ( 598 × 403 ) / 13
LCM(598,403) = 240994 / 13
LCM(598,403) = 18538
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FAQs on GCF of Fractions of 8417/598, 9720/403
1. What is the HCF of 8417,9720?
The HCF of 8417,9720 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 8417/598, 9720/403?
Answer: GCF of Numerators as per given numbers 8417/598, 9720/403 is
GCF of Numerators i.e. for 8417,9720 is 1
LCM of denominators i.e. for 598,403 is 18538.
Thus, GCF of Fractions is 1/18538.Finally, GCF of Fractions for 8417/598, 9720/403 is 1/18538.