GCF of 972/164, 5200/409
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 972/164, 5200/409 i.e 4/67076 easily. The following is the detailed procedure to determine the greatest common factor of fractions 972/164, 5200/409.
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 972/164,5200/409?
Given fractions are 972/164,5200/409
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 972/164,5200/409, numerators are 972,5200
Denominators are 164,409
The GCF of 972,5200 is 4 .
LCM of 164,409 is 67076.
The greatest common factor of 972/164,5200/409 = [GCF of 972,5200]/[LCM of 164,409]= 4/67076
Therefore, the GCF of 972/164,5200/409 is 4/67076.
To find the highest common factor of 972,5200, we have to find the factors of both numbers and list the highest common factor.
The factors of 972 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 243, 324, 486, 972
The factors of 5200 are 1, 2, 4, 5, 8, 10, 13, 16, 20, 25, 26, 40, 50, 52, 65, 80, 100, 104, 130, 200, 208, 260, 325, 400, 520, 650, 1040, 1300, 2600, 5200
The HCF of 972,5200 is 4.
Lets's calculate GCF of 972,5200
| 2 | 972, 5200 |
| 2 | 486, 2600 |
| 243, 1300 |
∴ So the GCF of the given numbers is 2 x 2 = 4
Greatest Common Factor of 972,5200 By Matching Biggest Common Factor Method
Now, list down the factors of 972
:1,2,3,4,6,9,12,18,27,36,54,81,108,162,243,324,486,972
Now, list down the factors of 5200
:1,2,4,5,8,10,13,16,20,25,26,40,50,52,65,80,100,104,130,200,208,260,325,400,520,650,1040,1300,2600,5200
Greatest Common Factor
We found the factors 972,5200 . The biggest common factor number is the GCF number.
So the greatest common factor 972,5200 is 4.
Lets's calculate LCM of 164,409
Given numbers has no common factors except 1. So, there LCM is their product i.e 67076
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/67076
Therefore, the GCF of Fractions 972/164,5200/409 is 4/67076
Least Common Multiple of 164,409 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 164,409 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(164,409) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(164,409) x common factors =1 x 1 = 1
LCM(164,409) = ( 164 × 409 ) / 1
LCM(164,409) = 67076 / 1
LCM(164,409) = 67076
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FAQs on GCF of Fractions of 972/164, 5200/409
1. What is the HCF of 972,5200?
The HCF of 972,5200 is 4
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 972/164, 5200/409?
Answer: GCF of Numerators as per given numbers 972/164, 5200/409 is
GCF of Numerators i.e. for 972,5200 is 4
LCM of denominators i.e. for 164,409 is 67076.
Thus, GCF of Fractions is 4/67076.Finally, GCF of Fractions for 972/164, 5200/409 is 4/67076.